id sid tid token lemma pos cord-326740-1fjr9qr4 1 1 key key NN cord-326740-1fjr9qr4 1 2 : : : cord-326740-1fjr9qr4 1 3 cord-326740 cord-326740 NNP cord-326740-1fjr9qr4 1 4 - - HYPH cord-326740-1fjr9qr4 1 5 1fjr9qr4 1fjr9qr4 CD cord-326740-1fjr9qr4 1 6 authors author NNS cord-326740-1fjr9qr4 1 7 : : : cord-326740-1fjr9qr4 1 8 Perlman Perlman NNP cord-326740-1fjr9qr4 1 9 , , , cord-326740-1fjr9qr4 1 10 Yael Yael NNP cord-326740-1fjr9qr4 1 11 ; ; : cord-326740-1fjr9qr4 1 12 Yechiali Yechiali NNP cord-326740-1fjr9qr4 1 13 , , , cord-326740-1fjr9qr4 1 14 Uri Uri NNP cord-326740-1fjr9qr4 1 15 title title NN cord-326740-1fjr9qr4 1 16 : : : cord-326740-1fjr9qr4 1 17 Reducing reduce VBG cord-326740-1fjr9qr4 1 18 Risk risk NN cord-326740-1fjr9qr4 1 19 of of IN cord-326740-1fjr9qr4 1 20 Infection Infection NNP cord-326740-1fjr9qr4 1 21 - - , cord-326740-1fjr9qr4 1 22 the the DT cord-326740-1fjr9qr4 1 23 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 1 24 Queueing Queueing NNP cord-326740-1fjr9qr4 1 25 Game Game NNP cord-326740-1fjr9qr4 1 26 date date NN cord-326740-1fjr9qr4 1 27 : : : cord-326740-1fjr9qr4 1 28 2020 2020 CD cord-326740-1fjr9qr4 1 29 - - HYPH cord-326740-1fjr9qr4 1 30 09 09 CD cord-326740-1fjr9qr4 1 31 - - HYPH cord-326740-1fjr9qr4 1 32 03 03 CD cord-326740-1fjr9qr4 1 33 journal journal NN cord-326740-1fjr9qr4 1 34 : : : cord-326740-1fjr9qr4 2 1 Saf Saf NNP cord-326740-1fjr9qr4 2 2 Sci Sci NNP cord-326740-1fjr9qr4 2 3 DOI DOI NNP cord-326740-1fjr9qr4 2 4 : : : cord-326740-1fjr9qr4 2 5 10.1016 10.1016 CD cord-326740-1fjr9qr4 2 6 / / SYM cord-326740-1fjr9qr4 2 7 j.ssci.2020.104987 j.ssci.2020.104987 CD cord-326740-1fjr9qr4 2 8 sha sha NNP cord-326740-1fjr9qr4 2 9 : : : cord-326740-1fjr9qr4 2 10 ec11e98b319dc93d3ccf3d9463f4758934bfc743 ec11e98b319dc93d3ccf3d9463f4758934bfc743 NNP cord-326740-1fjr9qr4 2 11 doc_id doc_id CD cord-326740-1fjr9qr4 2 12 : : : cord-326740-1fjr9qr4 2 13 326740 326740 CD cord-326740-1fjr9qr4 2 14 cord_uid cord_uid NNS cord-326740-1fjr9qr4 2 15 : : : cord-326740-1fjr9qr4 2 16 1fjr9qr4 1fjr9qr4 CD cord-326740-1fjr9qr4 3 1 The the DT cord-326740-1fjr9qr4 3 2 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 3 3 pandemic pandemic NN cord-326740-1fjr9qr4 3 4 has have VBZ cord-326740-1fjr9qr4 3 5 forced force VBN cord-326740-1fjr9qr4 3 6 numerous numerous JJ cord-326740-1fjr9qr4 3 7 businesses business NNS cord-326740-1fjr9qr4 3 8 such such JJ cord-326740-1fjr9qr4 3 9 as as IN cord-326740-1fjr9qr4 3 10 department department NN cord-326740-1fjr9qr4 3 11 stores store NNS cord-326740-1fjr9qr4 3 12 and and CC cord-326740-1fjr9qr4 3 13 supermarkets supermarket NNS cord-326740-1fjr9qr4 3 14 to to TO cord-326740-1fjr9qr4 3 15 limit limit VB cord-326740-1fjr9qr4 3 16 the the DT cord-326740-1fjr9qr4 3 17 number number NN cord-326740-1fjr9qr4 3 18 of of IN cord-326740-1fjr9qr4 3 19 shoppers shopper NNS cord-326740-1fjr9qr4 3 20 inside inside IN cord-326740-1fjr9qr4 3 21 the the DT cord-326740-1fjr9qr4 3 22 store store NN cord-326740-1fjr9qr4 3 23 at at IN cord-326740-1fjr9qr4 3 24 any any DT cord-326740-1fjr9qr4 3 25 given give VBN cord-326740-1fjr9qr4 3 26 time time NN cord-326740-1fjr9qr4 3 27 to to TO cord-326740-1fjr9qr4 3 28 minimize minimize VB cord-326740-1fjr9qr4 3 29 infection infection NN cord-326740-1fjr9qr4 3 30 rates rate NNS cord-326740-1fjr9qr4 3 31 . . . cord-326740-1fjr9qr4 4 1 We -PRON- PRP cord-326740-1fjr9qr4 4 2 construct construct VBP cord-326740-1fjr9qr4 4 3 and and CC cord-326740-1fjr9qr4 4 4 analyze analyze VB cord-326740-1fjr9qr4 4 5 two two CD cord-326740-1fjr9qr4 4 6 models model NNS cord-326740-1fjr9qr4 4 7 designed design VBN cord-326740-1fjr9qr4 4 8 to to TO cord-326740-1fjr9qr4 4 9 optimize optimize VB cord-326740-1fjr9qr4 4 10 queue queue NN cord-326740-1fjr9qr4 4 11 sizes size NNS cord-326740-1fjr9qr4 4 12 and and CC cord-326740-1fjr9qr4 4 13 customer customer NN cord-326740-1fjr9qr4 4 14 waiting waiting NN cord-326740-1fjr9qr4 4 15 times time NNS cord-326740-1fjr9qr4 4 16 to to TO cord-326740-1fjr9qr4 4 17 ensure ensure VB cord-326740-1fjr9qr4 4 18 safety safety NN cord-326740-1fjr9qr4 4 19 . . . cord-326740-1fjr9qr4 5 1 In in IN cord-326740-1fjr9qr4 5 2 both both DT cord-326740-1fjr9qr4 5 3 models model NNS cord-326740-1fjr9qr4 5 4 , , , cord-326740-1fjr9qr4 5 5 customers customer NNS cord-326740-1fjr9qr4 5 6 arrive arrive VBP cord-326740-1fjr9qr4 5 7 randomly randomly RB cord-326740-1fjr9qr4 5 8 at at IN cord-326740-1fjr9qr4 5 9 the the DT cord-326740-1fjr9qr4 5 10 store store NN cord-326740-1fjr9qr4 5 11 and and CC cord-326740-1fjr9qr4 5 12 , , , cord-326740-1fjr9qr4 5 13 after after IN cord-326740-1fjr9qr4 5 14 receiving receive VBG cord-326740-1fjr9qr4 5 15 permission permission NN cord-326740-1fjr9qr4 5 16 to to TO cord-326740-1fjr9qr4 5 17 enter enter VB cord-326740-1fjr9qr4 5 18 , , , cord-326740-1fjr9qr4 5 19 pass pass VB cord-326740-1fjr9qr4 5 20 through through IN cord-326740-1fjr9qr4 5 21 two two CD cord-326740-1fjr9qr4 5 22 service service NN cord-326740-1fjr9qr4 5 23 phases phase NNS cord-326740-1fjr9qr4 5 24 : : : cord-326740-1fjr9qr4 5 25 shopping shopping NN cord-326740-1fjr9qr4 5 26 and and CC cord-326740-1fjr9qr4 5 27 payment payment NN cord-326740-1fjr9qr4 5 28 . . . cord-326740-1fjr9qr4 6 1 Each each DT cord-326740-1fjr9qr4 6 2 customer customer NN cord-326740-1fjr9qr4 6 3 spends spend VBZ cord-326740-1fjr9qr4 6 4 a a DT cord-326740-1fjr9qr4 6 5 random random JJ cord-326740-1fjr9qr4 6 6 period period NN cord-326740-1fjr9qr4 6 7 of of IN cord-326740-1fjr9qr4 6 8 time time NN cord-326740-1fjr9qr4 6 9 shopping shopping NN cord-326740-1fjr9qr4 6 10 ( ( -LRB- cord-326740-1fjr9qr4 6 11 first first JJ cord-326740-1fjr9qr4 6 12 phase phase NN cord-326740-1fjr9qr4 6 13 ) ) -RRB- cord-326740-1fjr9qr4 6 14 and and CC cord-326740-1fjr9qr4 6 15 then then RB cord-326740-1fjr9qr4 6 16 proceeds proceed VBZ cord-326740-1fjr9qr4 6 17 to to IN cord-326740-1fjr9qr4 6 18 the the DT cord-326740-1fjr9qr4 6 19 payment payment NN cord-326740-1fjr9qr4 6 20 area area NN cord-326740-1fjr9qr4 6 21 of of IN cord-326740-1fjr9qr4 6 22 the the DT cord-326740-1fjr9qr4 6 23 store store NN cord-326740-1fjr9qr4 6 24 ( ( -LRB- cord-326740-1fjr9qr4 6 25 second second JJ cord-326740-1fjr9qr4 6 26 phase phase NN cord-326740-1fjr9qr4 6 27 ) ) -RRB- cord-326740-1fjr9qr4 6 28 where where WRB cord-326740-1fjr9qr4 6 29 cashiers cashier NNS cord-326740-1fjr9qr4 6 30 are be VBP cord-326740-1fjr9qr4 6 31 assigned assign VBN cord-326740-1fjr9qr4 6 32 to to TO cord-326740-1fjr9qr4 6 33 serve serve VB cord-326740-1fjr9qr4 6 34 customers customer NNS cord-326740-1fjr9qr4 6 35 . . . cord-326740-1fjr9qr4 7 1 We -PRON- PRP cord-326740-1fjr9qr4 7 2 propose propose VBP cord-326740-1fjr9qr4 7 3 a a DT cord-326740-1fjr9qr4 7 4 novel novel JJ cord-326740-1fjr9qr4 7 5 approach approach NN cord-326740-1fjr9qr4 7 6 by by IN cord-326740-1fjr9qr4 7 7 which which WDT cord-326740-1fjr9qr4 7 8 to to TO cord-326740-1fjr9qr4 7 9 calculate calculate VB cord-326740-1fjr9qr4 7 10 the the DT cord-326740-1fjr9qr4 7 11 risk risk NN cord-326740-1fjr9qr4 7 12 of of IN cord-326740-1fjr9qr4 7 13 a a DT cord-326740-1fjr9qr4 7 14 customer customer NN cord-326740-1fjr9qr4 7 15 being be VBG cord-326740-1fjr9qr4 7 16 infected infect VBN cord-326740-1fjr9qr4 7 17 while while IN cord-326740-1fjr9qr4 7 18 queueing queue VBG cord-326740-1fjr9qr4 7 19 outside outside IN cord-326740-1fjr9qr4 7 20 the the DT cord-326740-1fjr9qr4 7 21 store store NN cord-326740-1fjr9qr4 7 22 , , , cord-326740-1fjr9qr4 7 23 while while IN cord-326740-1fjr9qr4 7 24 shopping shopping NN cord-326740-1fjr9qr4 7 25 , , , cord-326740-1fjr9qr4 7 26 and and CC cord-326740-1fjr9qr4 7 27 while while IN cord-326740-1fjr9qr4 7 28 checking check VBG cord-326740-1fjr9qr4 7 29 out out RP cord-326740-1fjr9qr4 7 30 with with IN cord-326740-1fjr9qr4 7 31 a a DT cord-326740-1fjr9qr4 7 32 cashier cashier NN cord-326740-1fjr9qr4 7 33 . . . cord-326740-1fjr9qr4 8 1 The the DT cord-326740-1fjr9qr4 8 2 risk risk NN cord-326740-1fjr9qr4 8 3 is be VBZ cord-326740-1fjr9qr4 8 4 proportional proportional JJ cord-326740-1fjr9qr4 8 5 to to IN cord-326740-1fjr9qr4 8 6 the the DT cord-326740-1fjr9qr4 8 7 second second JJ cord-326740-1fjr9qr4 8 8 factorial factorial JJ cord-326740-1fjr9qr4 8 9 moment moment NN cord-326740-1fjr9qr4 8 10 of of IN cord-326740-1fjr9qr4 8 11 the the DT cord-326740-1fjr9qr4 8 12 number number NN cord-326740-1fjr9qr4 8 13 of of IN cord-326740-1fjr9qr4 8 14 customers customer NNS cord-326740-1fjr9qr4 8 15 occupying occupy VBG cord-326740-1fjr9qr4 8 16 the the DT cord-326740-1fjr9qr4 8 17 space space NN cord-326740-1fjr9qr4 8 18 in in IN cord-326740-1fjr9qr4 8 19 each each DT cord-326740-1fjr9qr4 8 20 phase phase NN cord-326740-1fjr9qr4 8 21 of of IN cord-326740-1fjr9qr4 8 22 the the DT cord-326740-1fjr9qr4 8 23 shopping shopping NN cord-326740-1fjr9qr4 8 24 route route NN cord-326740-1fjr9qr4 8 25 . . . cord-326740-1fjr9qr4 9 1 We -PRON- PRP cord-326740-1fjr9qr4 9 2 derive derive VBP cord-326740-1fjr9qr4 9 3 equilibrium equilibrium NN cord-326740-1fjr9qr4 9 4 strategies strategy NNS cord-326740-1fjr9qr4 9 5 for for IN cord-326740-1fjr9qr4 9 6 a a DT cord-326740-1fjr9qr4 9 7 Stackelberg Stackelberg NNP cord-326740-1fjr9qr4 9 8 game game NN cord-326740-1fjr9qr4 9 9 in in IN cord-326740-1fjr9qr4 9 10 which which WDT cord-326740-1fjr9qr4 9 11 the the DT cord-326740-1fjr9qr4 9 12 authority authority NN cord-326740-1fjr9qr4 9 13 acts act VBZ cord-326740-1fjr9qr4 9 14 as as IN cord-326740-1fjr9qr4 9 15 a a DT cord-326740-1fjr9qr4 9 16 leader leader NN cord-326740-1fjr9qr4 9 17 who who WP cord-326740-1fjr9qr4 9 18 first first RB cord-326740-1fjr9qr4 9 19 chooses choose VBZ cord-326740-1fjr9qr4 9 20 the the DT cord-326740-1fjr9qr4 9 21 maximum maximum JJ cord-326740-1fjr9qr4 9 22 number number NN cord-326740-1fjr9qr4 9 23 of of IN cord-326740-1fjr9qr4 9 24 customers customer NNS cord-326740-1fjr9qr4 9 25 allowed allow VBN cord-326740-1fjr9qr4 9 26 inside inside IN cord-326740-1fjr9qr4 9 27 the the DT cord-326740-1fjr9qr4 9 28 store store NN cord-326740-1fjr9qr4 9 29 to to TO cord-326740-1fjr9qr4 9 30 minimize minimize VB cord-326740-1fjr9qr4 9 31 the the DT cord-326740-1fjr9qr4 9 32 risk risk NN cord-326740-1fjr9qr4 9 33 of of IN cord-326740-1fjr9qr4 9 34 infection infection NN cord-326740-1fjr9qr4 9 35 . . . cord-326740-1fjr9qr4 10 1 In in IN cord-326740-1fjr9qr4 10 2 the the DT cord-326740-1fjr9qr4 10 3 first first JJ cord-326740-1fjr9qr4 10 4 model model NN cord-326740-1fjr9qr4 10 5 , , , cord-326740-1fjr9qr4 10 6 store store NN cord-326740-1fjr9qr4 10 7 ’ ' '' cord-326740-1fjr9qr4 10 8 management management NN cord-326740-1fjr9qr4 10 9 chooses choose VBZ cord-326740-1fjr9qr4 10 10 the the DT cord-326740-1fjr9qr4 10 11 number number NN cord-326740-1fjr9qr4 10 12 of of IN cord-326740-1fjr9qr4 10 13 cashiers cashier NNS cord-326740-1fjr9qr4 10 14 to to TO cord-326740-1fjr9qr4 10 15 provide provide VB cord-326740-1fjr9qr4 10 16 to to TO cord-326740-1fjr9qr4 10 17 minimize minimize VB cord-326740-1fjr9qr4 10 18 its -PRON- PRP$ cord-326740-1fjr9qr4 10 19 operational operational JJ cord-326740-1fjr9qr4 10 20 costs cost NNS cord-326740-1fjr9qr4 10 21 and and CC cord-326740-1fjr9qr4 10 22 its -PRON- PRP$ cord-326740-1fjr9qr4 10 23 customers customer NNS cord-326740-1fjr9qr4 10 24 ’ ' '' cord-326740-1fjr9qr4 10 25 implied imply VBD cord-326740-1fjr9qr4 10 26 waiting waiting NN cord-326740-1fjr9qr4 10 27 costs cost NNS cord-326740-1fjr9qr4 10 28 based base VBN cord-326740-1fjr9qr4 10 29 on on IN cord-326740-1fjr9qr4 10 30 the the DT cord-326740-1fjr9qr4 10 31 number number NN cord-326740-1fjr9qr4 10 32 allowed allow VBN cord-326740-1fjr9qr4 10 33 in in IN cord-326740-1fjr9qr4 10 34 the the DT cord-326740-1fjr9qr4 10 35 store store NN cord-326740-1fjr9qr4 10 36 . . . cord-326740-1fjr9qr4 11 1 In in IN cord-326740-1fjr9qr4 11 2 the the DT cord-326740-1fjr9qr4 11 3 second second JJ cord-326740-1fjr9qr4 11 4 model model NN cord-326740-1fjr9qr4 11 5 , , , cord-326740-1fjr9qr4 11 6 the the DT cord-326740-1fjr9qr4 11 7 store store NN cord-326740-1fjr9qr4 11 8 partitions partition VBZ cord-326740-1fjr9qr4 11 9 its -PRON- PRP$ cord-326740-1fjr9qr4 11 10 total total JJ cord-326740-1fjr9qr4 11 11 space space NN cord-326740-1fjr9qr4 11 12 into into IN cord-326740-1fjr9qr4 11 13 two two CD cord-326740-1fjr9qr4 11 14 separate separate JJ cord-326740-1fjr9qr4 11 15 areas area NNS cord-326740-1fjr9qr4 11 16 – – : cord-326740-1fjr9qr4 11 17 one one CD cord-326740-1fjr9qr4 11 18 for for IN cord-326740-1fjr9qr4 11 19 shoppers shopper NNS cord-326740-1fjr9qr4 11 20 and and CC cord-326740-1fjr9qr4 11 21 one one CD cord-326740-1fjr9qr4 11 22 for for IN cord-326740-1fjr9qr4 11 23 the the DT cord-326740-1fjr9qr4 11 24 cashiers cashier NNS cord-326740-1fjr9qr4 11 25 and and CC cord-326740-1fjr9qr4 11 26 payers payer NNS cord-326740-1fjr9qr4 11 27 – – : cord-326740-1fjr9qr4 11 28 to to TO cord-326740-1fjr9qr4 11 29 increase increase VB cord-326740-1fjr9qr4 11 30 cashiers cashier NNS cord-326740-1fjr9qr4 11 31 ’ ' '' cord-326740-1fjr9qr4 11 32 safety safety NN cord-326740-1fjr9qr4 11 33 . . . cord-326740-1fjr9qr4 12 1 Our -PRON- PRP$ cord-326740-1fjr9qr4 12 2 findings finding NNS cord-326740-1fjr9qr4 12 3 and and CC cord-326740-1fjr9qr4 12 4 analysis analysis NN cord-326740-1fjr9qr4 12 5 are be VBP cord-326740-1fjr9qr4 12 6 useful useful JJ cord-326740-1fjr9qr4 12 7 and and CC cord-326740-1fjr9qr4 12 8 applicable applicable JJ cord-326740-1fjr9qr4 12 9 for for IN cord-326740-1fjr9qr4 12 10 authorities authority NNS cord-326740-1fjr9qr4 12 11 and and CC cord-326740-1fjr9qr4 12 12 businesses business NNS cord-326740-1fjr9qr4 12 13 alike alike RB cord-326740-1fjr9qr4 12 14 in in IN cord-326740-1fjr9qr4 12 15 their -PRON- PRP$ cord-326740-1fjr9qr4 12 16 efforts effort NNS cord-326740-1fjr9qr4 12 17 to to TO cord-326740-1fjr9qr4 12 18 protect protect VB cord-326740-1fjr9qr4 12 19 both both DT cord-326740-1fjr9qr4 12 20 customers customer NNS cord-326740-1fjr9qr4 12 21 and and CC cord-326740-1fjr9qr4 12 22 employees employee NNS cord-326740-1fjr9qr4 12 23 while while IN cord-326740-1fjr9qr4 12 24 reducing reduce VBG cord-326740-1fjr9qr4 12 25 associated associate VBN cord-326740-1fjr9qr4 12 26 costs cost NNS cord-326740-1fjr9qr4 12 27 . . . cord-326740-1fjr9qr4 13 1 The the DT cord-326740-1fjr9qr4 13 2 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 13 3 pandemic pandemic NN cord-326740-1fjr9qr4 13 4 has have VBZ cord-326740-1fjr9qr4 13 5 upended upend VBN cord-326740-1fjr9qr4 13 6 nearly nearly RB cord-326740-1fjr9qr4 13 7 every every DT cord-326740-1fjr9qr4 13 8 type type NN cord-326740-1fjr9qr4 13 9 of of IN cord-326740-1fjr9qr4 13 10 business business NN cord-326740-1fjr9qr4 13 11 , , , cord-326740-1fjr9qr4 13 12 but but CC cord-326740-1fjr9qr4 13 13 one one CD cord-326740-1fjr9qr4 13 14 of of IN cord-326740-1fjr9qr4 13 15 the the DT cord-326740-1fjr9qr4 13 16 more more RBR cord-326740-1fjr9qr4 13 17 dramatic dramatic JJ cord-326740-1fjr9qr4 13 18 impacts impact NNS cord-326740-1fjr9qr4 13 19 early early RB cord-326740-1fjr9qr4 13 20 in in IN cord-326740-1fjr9qr4 13 21 the the DT cord-326740-1fjr9qr4 13 22 pandemic pandemic NN cord-326740-1fjr9qr4 13 23 has have VBZ cord-326740-1fjr9qr4 13 24 been be VBN cord-326740-1fjr9qr4 13 25 long long JJ cord-326740-1fjr9qr4 13 26 queues queue NNS cord-326740-1fjr9qr4 13 27 of of IN cord-326740-1fjr9qr4 13 28 customers customer NNS cord-326740-1fjr9qr4 13 29 outside outside IN cord-326740-1fjr9qr4 13 30 supermarkets supermarket NNS cord-326740-1fjr9qr4 13 31 . . . cord-326740-1fjr9qr4 14 1 The the DT cord-326740-1fjr9qr4 14 2 need need NN cord-326740-1fjr9qr4 14 3 to to TO cord-326740-1fjr9qr4 14 4 reduce reduce VB cord-326740-1fjr9qr4 14 5 crowding crowding NN cord-326740-1fjr9qr4 14 6 and and CC cord-326740-1fjr9qr4 14 7 queueing queueing NN cord-326740-1fjr9qr4 14 8 has have VBZ cord-326740-1fjr9qr4 14 9 forced force VBN cord-326740-1fjr9qr4 14 10 store store NN cord-326740-1fjr9qr4 14 11 managers manager NNS cord-326740-1fjr9qr4 14 12 worldwide worldwide RB cord-326740-1fjr9qr4 14 13 to to TO cord-326740-1fjr9qr4 14 14 implement implement VB cord-326740-1fjr9qr4 14 15 regulations regulation NNS cord-326740-1fjr9qr4 14 16 such such JJ cord-326740-1fjr9qr4 14 17 as as IN cord-326740-1fjr9qr4 14 18 " " `` cord-326740-1fjr9qr4 14 19 maximum maximum JJ cord-326740-1fjr9qr4 14 20 shoppers shopper NNS cord-326740-1fjr9qr4 14 21 at at IN cord-326740-1fjr9qr4 14 22 store store NN cord-326740-1fjr9qr4 14 23 " " '' cord-326740-1fjr9qr4 14 24 and and CC cord-326740-1fjr9qr4 14 25 " " `` cord-326740-1fjr9qr4 14 26 maximum maximum JJ cord-326740-1fjr9qr4 14 27 number number NN cord-326740-1fjr9qr4 14 28 of of IN cord-326740-1fjr9qr4 14 29 customers customer NNS cord-326740-1fjr9qr4 14 30 in in IN cord-326740-1fjr9qr4 14 31 checkout checkout NN cord-326740-1fjr9qr4 14 32 areas area NNS cord-326740-1fjr9qr4 14 33 . . . cord-326740-1fjr9qr4 14 34 " " '' cord-326740-1fjr9qr4 15 1 According accord VBG cord-326740-1fjr9qr4 15 2 to to IN cord-326740-1fjr9qr4 15 3 a a DT cord-326740-1fjr9qr4 15 4 recent recent JJ cord-326740-1fjr9qr4 15 5 report report NN cord-326740-1fjr9qr4 15 6 by by IN cord-326740-1fjr9qr4 15 7 BBC BBC NNP cord-326740-1fjr9qr4 15 8 News News NNP cord-326740-1fjr9qr4 15 9 ( ( -LRB- cord-326740-1fjr9qr4 15 10 2020 2020 CD cord-326740-1fjr9qr4 15 11 ) ) -RRB- cord-326740-1fjr9qr4 15 12 , , , cord-326740-1fjr9qr4 15 13 supermarkets supermarket NNS cord-326740-1fjr9qr4 15 14 in in IN cord-326740-1fjr9qr4 15 15 the the DT cord-326740-1fjr9qr4 15 16 United United NNP cord-326740-1fjr9qr4 15 17 Kingdom Kingdom NNP cord-326740-1fjr9qr4 15 18 are be VBP cord-326740-1fjr9qr4 15 19 posting post VBG cord-326740-1fjr9qr4 15 20 staff staff NN cord-326740-1fjr9qr4 15 21 members member NNS cord-326740-1fjr9qr4 15 22 at at IN cord-326740-1fjr9qr4 15 23 the the DT cord-326740-1fjr9qr4 15 24 doors door NNS cord-326740-1fjr9qr4 15 25 who who WP cord-326740-1fjr9qr4 15 26 allow allow VBP cord-326740-1fjr9qr4 15 27 a a DT cord-326740-1fjr9qr4 15 28 maximum maximum NN cord-326740-1fjr9qr4 15 29 of of IN cord-326740-1fjr9qr4 15 30 75 75 CD cord-326740-1fjr9qr4 15 31 shoppers shopper NNS cord-326740-1fjr9qr4 15 32 inside inside IN cord-326740-1fjr9qr4 15 33 the the DT cord-326740-1fjr9qr4 15 34 store store NN cord-326740-1fjr9qr4 15 35 at at IN cord-326740-1fjr9qr4 15 36 a a DT cord-326740-1fjr9qr4 15 37 time time NN cord-326740-1fjr9qr4 15 38 . . . cord-326740-1fjr9qr4 16 1 Israeli israeli JJ cord-326740-1fjr9qr4 16 2 i24News i24news XX cord-326740-1fjr9qr4 17 1 ( ( -LRB- cord-326740-1fjr9qr4 17 2 2020 2020 CD cord-326740-1fjr9qr4 17 3 ) ) -RRB- cord-326740-1fjr9qr4 17 4 reports report VBZ cord-326740-1fjr9qr4 17 5 that that IN cord-326740-1fjr9qr4 17 6 all all DT cord-326740-1fjr9qr4 17 7 business business NN cord-326740-1fjr9qr4 17 8 owners owner NNS cord-326740-1fjr9qr4 17 9 in in IN cord-326740-1fjr9qr4 17 10 Israel Israel NNP cord-326740-1fjr9qr4 17 11 are be VBP cord-326740-1fjr9qr4 17 12 required require VBN cord-326740-1fjr9qr4 17 13 to to TO cord-326740-1fjr9qr4 17 14 place place VB cord-326740-1fjr9qr4 17 15 signs sign NNS cord-326740-1fjr9qr4 17 16 at at IN cord-326740-1fjr9qr4 17 17 store store NN cord-326740-1fjr9qr4 17 18 entrances entrance NNS cord-326740-1fjr9qr4 17 19 specifying specify VBG cord-326740-1fjr9qr4 17 20 the the DT cord-326740-1fjr9qr4 17 21 maximum maximum JJ cord-326740-1fjr9qr4 17 22 number number NN cord-326740-1fjr9qr4 17 23 of of IN cord-326740-1fjr9qr4 17 24 people people NNS cord-326740-1fjr9qr4 17 25 allowed allow VBN cord-326740-1fjr9qr4 17 26 on on IN cord-326740-1fjr9qr4 17 27 the the DT cord-326740-1fjr9qr4 17 28 premises premise NNS cord-326740-1fjr9qr4 17 29 . . . cord-326740-1fjr9qr4 18 1 As as IN cord-326740-1fjr9qr4 18 2 a a DT cord-326740-1fjr9qr4 18 3 result result NN cord-326740-1fjr9qr4 18 4 of of IN cord-326740-1fjr9qr4 18 5 these these DT cord-326740-1fjr9qr4 18 6 maximum maximum JJ cord-326740-1fjr9qr4 18 7 headcount headcount NN cord-326740-1fjr9qr4 18 8 policies policy NNS cord-326740-1fjr9qr4 18 9 , , , cord-326740-1fjr9qr4 18 10 sometimes sometimes RB cord-326740-1fjr9qr4 18 11 - - HYPH cord-326740-1fjr9qr4 18 12 long long JJ cord-326740-1fjr9qr4 18 13 queues queue NNS cord-326740-1fjr9qr4 18 14 are be VBP cord-326740-1fjr9qr4 18 15 forming form VBG cord-326740-1fjr9qr4 18 16 outside outside IN cord-326740-1fjr9qr4 18 17 these these DT cord-326740-1fjr9qr4 18 18 businesses business NNS cord-326740-1fjr9qr4 18 19 . . . cord-326740-1fjr9qr4 19 1 Evidence evidence NN cord-326740-1fjr9qr4 19 2 is be VBZ cord-326740-1fjr9qr4 19 3 growing grow VBG cord-326740-1fjr9qr4 19 4 that that DT cord-326740-1fjr9qr4 19 5 infection infection NN cord-326740-1fjr9qr4 19 6 with with IN cord-326740-1fjr9qr4 19 7 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 19 8 is be VBZ cord-326740-1fjr9qr4 19 9 associated associate VBN cord-326740-1fjr9qr4 19 10 with with IN cord-326740-1fjr9qr4 19 11 prolonged prolonged JJ cord-326740-1fjr9qr4 19 12 periods period NNS cord-326740-1fjr9qr4 19 13 of of IN cord-326740-1fjr9qr4 19 14 exposure exposure NN cord-326740-1fjr9qr4 19 15 to to IN cord-326740-1fjr9qr4 19 16 infected infect VBN cord-326740-1fjr9qr4 19 17 individuals individual NNS cord-326740-1fjr9qr4 19 18 ( ( -LRB- cord-326740-1fjr9qr4 19 19 CNN CNN NNP cord-326740-1fjr9qr4 19 20 , , , cord-326740-1fjr9qr4 19 21 2020 2020 CD cord-326740-1fjr9qr4 19 22 ) ) -RRB- cord-326740-1fjr9qr4 19 23 . . . cord-326740-1fjr9qr4 20 1 The the DT cord-326740-1fjr9qr4 20 2 longer long JJR cord-326740-1fjr9qr4 20 3 one one NN cord-326740-1fjr9qr4 20 4 spends spend VBZ cord-326740-1fjr9qr4 20 5 in in IN cord-326740-1fjr9qr4 20 6 a a DT cord-326740-1fjr9qr4 20 7 crowded crowded JJ cord-326740-1fjr9qr4 20 8 environment environment NN cord-326740-1fjr9qr4 20 9 with with IN cord-326740-1fjr9qr4 20 10 people people NNS cord-326740-1fjr9qr4 20 11 who who WP cord-326740-1fjr9qr4 20 12 may may MD cord-326740-1fjr9qr4 20 13 be be VB cord-326740-1fjr9qr4 20 14 infected infect VBN cord-326740-1fjr9qr4 20 15 , , , cord-326740-1fjr9qr4 20 16 the the DT cord-326740-1fjr9qr4 20 17 greater great JJR cord-326740-1fjr9qr4 20 18 the the DT cord-326740-1fjr9qr4 20 19 risk risk NN cord-326740-1fjr9qr4 20 20 of of IN cord-326740-1fjr9qr4 20 21 getting get VBG cord-326740-1fjr9qr4 20 22 sick sick JJ cord-326740-1fjr9qr4 20 23 ( ( -LRB- cord-326740-1fjr9qr4 20 24 Barr Barr NNP cord-326740-1fjr9qr4 20 25 , , , cord-326740-1fjr9qr4 20 26 2020 2020 CD cord-326740-1fjr9qr4 20 27 ) ) -RRB- cord-326740-1fjr9qr4 20 28 . . . cord-326740-1fjr9qr4 21 1 Therefore therefore RB cord-326740-1fjr9qr4 21 2 , , , cord-326740-1fjr9qr4 21 3 greater great JJR cord-326740-1fjr9qr4 21 4 numbers number NNS cord-326740-1fjr9qr4 21 5 of of IN cord-326740-1fjr9qr4 21 6 people people NNS cord-326740-1fjr9qr4 21 7 in in IN cord-326740-1fjr9qr4 21 8 stores store NNS cord-326740-1fjr9qr4 21 9 and and CC cord-326740-1fjr9qr4 21 10 queues queue NNS cord-326740-1fjr9qr4 21 11 increase increase VBP cord-326740-1fjr9qr4 21 12 the the DT cord-326740-1fjr9qr4 21 13 likelihood likelihood NN cord-326740-1fjr9qr4 21 14 of of IN cord-326740-1fjr9qr4 21 15 infection infection NN cord-326740-1fjr9qr4 21 16 and and CC cord-326740-1fjr9qr4 21 17 make make VB cord-326740-1fjr9qr4 21 18 it -PRON- PRP cord-326740-1fjr9qr4 21 19 difficult difficult JJ cord-326740-1fjr9qr4 21 20 to to TO cord-326740-1fjr9qr4 21 21 ensure ensure VB cord-326740-1fjr9qr4 21 22 that that IN cord-326740-1fjr9qr4 21 23 social social JJ cord-326740-1fjr9qr4 21 24 distancing distancing NN cord-326740-1fjr9qr4 21 25 restrictions restriction NNS cord-326740-1fjr9qr4 21 26 are be VBP cord-326740-1fjr9qr4 21 27 maintained maintain VBN cord-326740-1fjr9qr4 22 1 ( ( -LRB- cord-326740-1fjr9qr4 22 2 Long long RB cord-326740-1fjr9qr4 22 3 et et NNP cord-326740-1fjr9qr4 22 4 al al NNP cord-326740-1fjr9qr4 22 5 . . NNP cord-326740-1fjr9qr4 22 6 , , , cord-326740-1fjr9qr4 22 7 2020 2020 CD cord-326740-1fjr9qr4 22 8 ) ) -RRB- cord-326740-1fjr9qr4 22 9 . . . cord-326740-1fjr9qr4 23 1 Customers customer NNS cord-326740-1fjr9qr4 23 2 waiting wait VBG cord-326740-1fjr9qr4 23 3 outside outside IN cord-326740-1fjr9qr4 23 4 of of IN cord-326740-1fjr9qr4 23 5 stores store NNS cord-326740-1fjr9qr4 23 6 can can MD cord-326740-1fjr9qr4 23 7 maintain maintain VB cord-326740-1fjr9qr4 23 8 adequate adequate JJ cord-326740-1fjr9qr4 23 9 social social JJ cord-326740-1fjr9qr4 23 10 distance distance NN cord-326740-1fjr9qr4 23 11 but but CC cord-326740-1fjr9qr4 23 12 are be VBP cord-326740-1fjr9qr4 23 13 still still RB cord-326740-1fjr9qr4 23 14 potentially potentially RB cord-326740-1fjr9qr4 23 15 exposed expose VBN cord-326740-1fjr9qr4 23 16 to to IN cord-326740-1fjr9qr4 23 17 infection infection NN cord-326740-1fjr9qr4 24 1 ( ( -LRB- cord-326740-1fjr9qr4 24 2 Gupta Gupta NNP cord-326740-1fjr9qr4 24 3 et et NNP cord-326740-1fjr9qr4 24 4 al al NNP cord-326740-1fjr9qr4 24 5 . . NNP cord-326740-1fjr9qr4 24 6 , , , cord-326740-1fjr9qr4 24 7 2020 2020 CD cord-326740-1fjr9qr4 24 8 ) ) -RRB- cord-326740-1fjr9qr4 24 9 . . . cord-326740-1fjr9qr4 25 1 It -PRON- PRP cord-326740-1fjr9qr4 25 2 is be VBZ cord-326740-1fjr9qr4 25 3 also also RB cord-326740-1fjr9qr4 25 4 critical critical JJ cord-326740-1fjr9qr4 25 5 to to TO cord-326740-1fjr9qr4 25 6 keep keep VB cord-326740-1fjr9qr4 25 7 workers worker NNS cord-326740-1fjr9qr4 25 8 safe safe JJ cord-326740-1fjr9qr4 25 9 during during IN cord-326740-1fjr9qr4 25 10 the the DT cord-326740-1fjr9qr4 25 11 pandemic pandemic NN cord-326740-1fjr9qr4 25 12 , , , cord-326740-1fjr9qr4 25 13 and and CC cord-326740-1fjr9qr4 25 14 greater great JJR cord-326740-1fjr9qr4 25 15 efforts effort NNS cord-326740-1fjr9qr4 25 16 are be VBP cord-326740-1fjr9qr4 25 17 needed need VBN cord-326740-1fjr9qr4 25 18 to to TO cord-326740-1fjr9qr4 25 19 reduce reduce VB cord-326740-1fjr9qr4 25 20 the the DT cord-326740-1fjr9qr4 25 21 number number NN cord-326740-1fjr9qr4 25 22 of of IN cord-326740-1fjr9qr4 25 23 customers customer NNS cord-326740-1fjr9qr4 25 24 waiting wait VBG cord-326740-1fjr9qr4 25 25 at at IN cord-326740-1fjr9qr4 25 26 cashier cashier NN cord-326740-1fjr9qr4 25 27 areas area NNS cord-326740-1fjr9qr4 25 28 to to TO cord-326740-1fjr9qr4 25 29 allow allow VB cord-326740-1fjr9qr4 25 30 employees employee NNS cord-326740-1fjr9qr4 25 31 to to TO cord-326740-1fjr9qr4 25 32 maintain maintain VB cord-326740-1fjr9qr4 25 33 social social JJ cord-326740-1fjr9qr4 25 34 distance distance NN cord-326740-1fjr9qr4 25 35 from from IN cord-326740-1fjr9qr4 25 36 customers customer NNS cord-326740-1fjr9qr4 25 37 ( ( -LRB- cord-326740-1fjr9qr4 25 38 see see UH cord-326740-1fjr9qr4 25 39 , , , cord-326740-1fjr9qr4 25 40 e.g. e.g. RB cord-326740-1fjr9qr4 25 41 , , , cord-326740-1fjr9qr4 25 42 Government Government NNP cord-326740-1fjr9qr4 25 43 of of IN cord-326740-1fjr9qr4 25 44 the the DT cord-326740-1fjr9qr4 25 45 United United NNP cord-326740-1fjr9qr4 25 46 Kingdom Kingdom NNP cord-326740-1fjr9qr4 25 47 ( ( -LRB- cord-326740-1fjr9qr4 25 48 2020 2020 CD cord-326740-1fjr9qr4 25 49 ) ) -RRB- cord-326740-1fjr9qr4 25 50 ) ) -RRB- cord-326740-1fjr9qr4 25 51 . . . cord-326740-1fjr9qr4 26 1 Thus thus RB cord-326740-1fjr9qr4 26 2 , , , cord-326740-1fjr9qr4 26 3 it -PRON- PRP cord-326740-1fjr9qr4 26 4 is be VBZ cord-326740-1fjr9qr4 26 5 critical critical JJ cord-326740-1fjr9qr4 26 6 to to TO cord-326740-1fjr9qr4 26 7 control control VB cord-326740-1fjr9qr4 26 8 and and CC cord-326740-1fjr9qr4 26 9 manage manage VB cord-326740-1fjr9qr4 26 10 queue queue NN cord-326740-1fjr9qr4 26 11 sizes size NNS cord-326740-1fjr9qr4 26 12 and and CC cord-326740-1fjr9qr4 26 13 customer customer NN cord-326740-1fjr9qr4 26 14 waiting waiting NN cord-326740-1fjr9qr4 26 15 times time NNS cord-326740-1fjr9qr4 26 16 to to TO cord-326740-1fjr9qr4 26 17 ensure ensure VB cord-326740-1fjr9qr4 26 18 the the DT cord-326740-1fjr9qr4 26 19 safety safety NN cord-326740-1fjr9qr4 26 20 of of IN cord-326740-1fjr9qr4 26 21 customers customer NNS cord-326740-1fjr9qr4 26 22 and and CC cord-326740-1fjr9qr4 26 23 workers worker NNS cord-326740-1fjr9qr4 26 24 . . . cord-326740-1fjr9qr4 27 1 Systems system NNS cord-326740-1fjr9qr4 27 2 for for IN cord-326740-1fjr9qr4 27 3 reducing reduce VBG cord-326740-1fjr9qr4 27 4 the the DT cord-326740-1fjr9qr4 27 5 number number NN cord-326740-1fjr9qr4 27 6 customers customer NNS cord-326740-1fjr9qr4 27 7 in in IN cord-326740-1fjr9qr4 27 8 retail retail JJ cord-326740-1fjr9qr4 27 9 stores store NNS cord-326740-1fjr9qr4 27 10 and and CC cord-326740-1fjr9qr4 27 11 reducing reduce VBG cord-326740-1fjr9qr4 27 12 waiting wait VBG cord-326740-1fjr9qr4 27 13 times time NNS cord-326740-1fjr9qr4 27 14 have have VBP cord-326740-1fjr9qr4 27 15 been be VBN cord-326740-1fjr9qr4 27 16 studied study VBN cord-326740-1fjr9qr4 27 17 intensively intensively RB cord-326740-1fjr9qr4 27 18 in in IN cord-326740-1fjr9qr4 27 19 the the DT cord-326740-1fjr9qr4 27 20 literature literature NN cord-326740-1fjr9qr4 27 21 using use VBG cord-326740-1fjr9qr4 27 22 queueing queue VBG cord-326740-1fjr9qr4 27 23 theory theory NN cord-326740-1fjr9qr4 27 24 . . . cord-326740-1fjr9qr4 28 1 Recently recently RB cord-326740-1fjr9qr4 28 2 , , , cord-326740-1fjr9qr4 28 3 several several JJ cord-326740-1fjr9qr4 28 4 queueing queueing NN cord-326740-1fjr9qr4 28 5 models model NNS cord-326740-1fjr9qr4 28 6 have have VBP cord-326740-1fjr9qr4 28 7 been be VBN cord-326740-1fjr9qr4 28 8 constructed construct VBN cord-326740-1fjr9qr4 28 9 to to TO cord-326740-1fjr9qr4 28 10 study study VB cord-326740-1fjr9qr4 28 11 the the DT cord-326740-1fjr9qr4 28 12 impact impact NN cord-326740-1fjr9qr4 28 13 of of IN cord-326740-1fjr9qr4 28 14 the the DT cord-326740-1fjr9qr4 28 15 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 28 16 pandemic pandemic NN cord-326740-1fjr9qr4 28 17 ( ( -LRB- cord-326740-1fjr9qr4 28 18 see see VB cord-326740-1fjr9qr4 28 19 , , , cord-326740-1fjr9qr4 28 20 e.g. e.g. RB cord-326740-1fjr9qr4 28 21 , , , cord-326740-1fjr9qr4 28 22 Kaplan Kaplan NNP cord-326740-1fjr9qr4 28 23 , , , cord-326740-1fjr9qr4 28 24 2020 2020 CD cord-326740-1fjr9qr4 28 25 ; ; : cord-326740-1fjr9qr4 28 26 Alban Alban NNP cord-326740-1fjr9qr4 28 27 et et NNP cord-326740-1fjr9qr4 28 28 al al NNP cord-326740-1fjr9qr4 28 29 . . . cord-326740-1fjr9qr4 29 1 , , , cord-326740-1fjr9qr4 29 2 2020 2020 CD cord-326740-1fjr9qr4 29 3 , , , cord-326740-1fjr9qr4 29 4 Long Long NNP cord-326740-1fjr9qr4 29 5 et et NNP cord-326740-1fjr9qr4 29 6 al al NNP cord-326740-1fjr9qr4 29 7 . . NNP cord-326740-1fjr9qr4 29 8 , , , cord-326740-1fjr9qr4 29 9 2020 2020 CD cord-326740-1fjr9qr4 29 10 . . . cord-326740-1fjr9qr4 30 1 In in IN cord-326740-1fjr9qr4 30 2 this this DT cord-326740-1fjr9qr4 30 3 paper paper NN cord-326740-1fjr9qr4 30 4 , , , cord-326740-1fjr9qr4 30 5 we -PRON- PRP cord-326740-1fjr9qr4 30 6 construct construct VBP cord-326740-1fjr9qr4 30 7 and and CC cord-326740-1fjr9qr4 30 8 analyze analyze VB cord-326740-1fjr9qr4 30 9 two two CD cord-326740-1fjr9qr4 30 10 models model NNS cord-326740-1fjr9qr4 30 11 to to TO cord-326740-1fjr9qr4 30 12 optimize optimize VB cord-326740-1fjr9qr4 30 13 queueing queueing NN cord-326740-1fjr9qr4 30 14 when when WRB cord-326740-1fjr9qr4 30 15 there there EX cord-326740-1fjr9qr4 30 16 is be VBZ cord-326740-1fjr9qr4 30 17 a a DT cord-326740-1fjr9qr4 30 18 limit limit NN cord-326740-1fjr9qr4 30 19 on on IN cord-326740-1fjr9qr4 30 20 the the DT cord-326740-1fjr9qr4 30 21 number number NN cord-326740-1fjr9qr4 30 22 of of IN cord-326740-1fjr9qr4 30 23 customers customer NNS cord-326740-1fjr9qr4 30 24 allowed allow VBN cord-326740-1fjr9qr4 30 25 inside inside IN cord-326740-1fjr9qr4 30 26 a a DT cord-326740-1fjr9qr4 30 27 store store NN cord-326740-1fjr9qr4 30 28 . . . cord-326740-1fjr9qr4 31 1 Customers customer NNS cord-326740-1fjr9qr4 31 2 arrive arrive VBP cord-326740-1fjr9qr4 31 3 randomly randomly RB cord-326740-1fjr9qr4 31 4 at at IN cord-326740-1fjr9qr4 31 5 the the DT cord-326740-1fjr9qr4 31 6 store store NN cord-326740-1fjr9qr4 31 7 and and CC cord-326740-1fjr9qr4 31 8 , , , cord-326740-1fjr9qr4 31 9 after after IN cord-326740-1fjr9qr4 31 10 receiving receive VBG cord-326740-1fjr9qr4 31 11 permission permission NN cord-326740-1fjr9qr4 31 12 to to TO cord-326740-1fjr9qr4 31 13 enter enter VB cord-326740-1fjr9qr4 31 14 , , , cord-326740-1fjr9qr4 31 15 pass pass VB cord-326740-1fjr9qr4 31 16 through through IN cord-326740-1fjr9qr4 31 17 two two CD cord-326740-1fjr9qr4 31 18 service service NN cord-326740-1fjr9qr4 31 19 phases phase NNS cord-326740-1fjr9qr4 31 20 : : : cord-326740-1fjr9qr4 31 21 shopping shopping NN cord-326740-1fjr9qr4 31 22 and and CC cord-326740-1fjr9qr4 31 23 payment payment NN cord-326740-1fjr9qr4 31 24 . . . cord-326740-1fjr9qr4 32 1 Each each DT cord-326740-1fjr9qr4 32 2 customer customer NN cord-326740-1fjr9qr4 32 3 first first RB cord-326740-1fjr9qr4 32 4 spends spend VBZ cord-326740-1fjr9qr4 32 5 a a DT cord-326740-1fjr9qr4 32 6 random random JJ cord-326740-1fjr9qr4 32 7 period period NN cord-326740-1fjr9qr4 32 8 of of IN cord-326740-1fjr9qr4 32 9 time time NN cord-326740-1fjr9qr4 32 10 shopping shopping NN cord-326740-1fjr9qr4 32 11 ( ( -LRB- cord-326740-1fjr9qr4 32 12 first first JJ cord-326740-1fjr9qr4 32 13 phase phase NN cord-326740-1fjr9qr4 32 14 ) ) -RRB- cord-326740-1fjr9qr4 32 15 and and CC cord-326740-1fjr9qr4 32 16 then then RB cord-326740-1fjr9qr4 32 17 proceeds proceed VBZ cord-326740-1fjr9qr4 32 18 to to IN cord-326740-1fjr9qr4 32 19 the the DT cord-326740-1fjr9qr4 32 20 payment payment NN cord-326740-1fjr9qr4 32 21 area area NN cord-326740-1fjr9qr4 32 22 of of IN cord-326740-1fjr9qr4 32 23 the the DT cord-326740-1fjr9qr4 32 24 store store NN cord-326740-1fjr9qr4 32 25 ( ( -LRB- cord-326740-1fjr9qr4 32 26 second second JJ cord-326740-1fjr9qr4 32 27 phase phase NN cord-326740-1fjr9qr4 32 28 ) ) -RRB- cord-326740-1fjr9qr4 32 29 where where WRB cord-326740-1fjr9qr4 32 30 cashiers cashier NNS cord-326740-1fjr9qr4 32 31 are be VBP cord-326740-1fjr9qr4 32 32 assigned assign VBN cord-326740-1fjr9qr4 32 33 to to TO cord-326740-1fjr9qr4 32 34 serve serve VB cord-326740-1fjr9qr4 32 35 customers customer NNS cord-326740-1fjr9qr4 32 36 . . . cord-326740-1fjr9qr4 33 1 When when WRB cord-326740-1fjr9qr4 33 2 the the DT cord-326740-1fjr9qr4 33 3 store store NN cord-326740-1fjr9qr4 33 4 is be VBZ cord-326740-1fjr9qr4 33 5 occupied occupy VBN cord-326740-1fjr9qr4 33 6 by by IN cord-326740-1fjr9qr4 33 7 the the DT cord-326740-1fjr9qr4 33 8 maximum maximum JJ cord-326740-1fjr9qr4 33 9 number number NN cord-326740-1fjr9qr4 33 10 of of IN cord-326740-1fjr9qr4 33 11 allowed allow VBN cord-326740-1fjr9qr4 33 12 customers customer NNS cord-326740-1fjr9qr4 33 13 , , , cord-326740-1fjr9qr4 33 14 newly newly RB cord-326740-1fjr9qr4 33 15 arriving arrive VBG cord-326740-1fjr9qr4 33 16 customers customer NNS cord-326740-1fjr9qr4 33 17 wait wait VBP cord-326740-1fjr9qr4 33 18 outside outside RB cord-326740-1fjr9qr4 33 19 in in IN cord-326740-1fjr9qr4 33 20 line line NN cord-326740-1fjr9qr4 33 21 until until IN cord-326740-1fjr9qr4 33 22 permitted permit VBN cord-326740-1fjr9qr4 33 23 to to TO cord-326740-1fjr9qr4 33 24 enter enter VB cord-326740-1fjr9qr4 33 25 . . . cord-326740-1fjr9qr4 34 1 In in IN cord-326740-1fjr9qr4 34 2 the the DT cord-326740-1fjr9qr4 34 3 first first JJ cord-326740-1fjr9qr4 34 4 model model NN cord-326740-1fjr9qr4 34 5 , , , cord-326740-1fjr9qr4 34 6 after after IN cord-326740-1fjr9qr4 34 7 completing complete VBG cord-326740-1fjr9qr4 34 8 shopping shopping NN cord-326740-1fjr9qr4 34 9 , , , cord-326740-1fjr9qr4 34 10 the the DT cord-326740-1fjr9qr4 34 11 customer customer NN cord-326740-1fjr9qr4 34 12 proceeds proceed VBZ cord-326740-1fjr9qr4 34 13 to to IN cord-326740-1fjr9qr4 34 14 the the DT cord-326740-1fjr9qr4 34 15 payment payment NN cord-326740-1fjr9qr4 34 16 phase phase NN cord-326740-1fjr9qr4 34 17 and and CC cord-326740-1fjr9qr4 34 18 either either RB cord-326740-1fjr9qr4 34 19 is be VBZ cord-326740-1fjr9qr4 34 20 served serve VBN cord-326740-1fjr9qr4 34 21 immediately immediately RB cord-326740-1fjr9qr4 34 22 by by IN cord-326740-1fjr9qr4 34 23 a a DT cord-326740-1fjr9qr4 34 24 free free JJ cord-326740-1fjr9qr4 34 25 cashier cashier NN cord-326740-1fjr9qr4 34 26 or or CC cord-326740-1fjr9qr4 34 27 waits wait VBZ cord-326740-1fjr9qr4 34 28 in in IN cord-326740-1fjr9qr4 34 29 a a DT cord-326740-1fjr9qr4 34 30 line line NN cord-326740-1fjr9qr4 34 31 forming form VBG cord-326740-1fjr9qr4 34 32 in in IN cord-326740-1fjr9qr4 34 33 front front NN cord-326740-1fjr9qr4 34 34 of of IN cord-326740-1fjr9qr4 34 35 the the DT cord-326740-1fjr9qr4 34 36 cashiers cashier NNS cord-326740-1fjr9qr4 34 37 . . . cord-326740-1fjr9qr4 35 1 In in IN cord-326740-1fjr9qr4 35 2 the the DT cord-326740-1fjr9qr4 35 3 second second JJ cord-326740-1fjr9qr4 35 4 model model NN cord-326740-1fjr9qr4 35 5 , , , cord-326740-1fjr9qr4 35 6 we -PRON- PRP cord-326740-1fjr9qr4 35 7 analyze analyze VBP cord-326740-1fjr9qr4 35 8 reducing reduce VBG cord-326740-1fjr9qr4 35 9 waiting wait VBG cord-326740-1fjr9qr4 35 10 time time NN cord-326740-1fjr9qr4 35 11 in in IN cord-326740-1fjr9qr4 35 12 the the DT cord-326740-1fjr9qr4 35 13 payment payment NN cord-326740-1fjr9qr4 35 14 queue queue NN cord-326740-1fjr9qr4 35 15 ( ( -LRB- cord-326740-1fjr9qr4 35 16 and and CC cord-326740-1fjr9qr4 35 17 ensuring ensure VBG cord-326740-1fjr9qr4 35 18 the the DT cord-326740-1fjr9qr4 35 19 safety safety NN cord-326740-1fjr9qr4 35 20 of of IN cord-326740-1fjr9qr4 35 21 cashiers cashier NNS cord-326740-1fjr9qr4 35 22 and and CC cord-326740-1fjr9qr4 35 23 customers customer NNS cord-326740-1fjr9qr4 35 24 ) ) -RRB- cord-326740-1fjr9qr4 35 25 by by IN cord-326740-1fjr9qr4 35 26 allowing allow VBG cord-326740-1fjr9qr4 35 27 store store NN cord-326740-1fjr9qr4 35 28 management management NN cord-326740-1fjr9qr4 35 29 to to TO cord-326740-1fjr9qr4 35 30 set set VB cord-326740-1fjr9qr4 35 31 aside aside RP cord-326740-1fjr9qr4 35 32 a a DT cord-326740-1fjr9qr4 35 33 separate separate JJ cord-326740-1fjr9qr4 35 34 waiting waiting NN cord-326740-1fjr9qr4 35 35 space space NN cord-326740-1fjr9qr4 35 36 with with IN cord-326740-1fjr9qr4 35 37 limited limited JJ cord-326740-1fjr9qr4 35 38 capacity capacity NN cord-326740-1fjr9qr4 35 39 adjacent adjacent JJ cord-326740-1fjr9qr4 35 40 to to IN cord-326740-1fjr9qr4 35 41 the the DT cord-326740-1fjr9qr4 35 42 cashiers cashier NNS cord-326740-1fjr9qr4 35 43 . . . cord-326740-1fjr9qr4 36 1 For for IN cord-326740-1fjr9qr4 36 2 each each DT cord-326740-1fjr9qr4 36 3 model model NN cord-326740-1fjr9qr4 36 4 , , , cord-326740-1fjr9qr4 36 5 we -PRON- PRP cord-326740-1fjr9qr4 36 6 derive derive VBP cord-326740-1fjr9qr4 36 7 the the DT cord-326740-1fjr9qr4 36 8 resulting result VBG cord-326740-1fjr9qr4 36 9 stability stability NN cord-326740-1fjr9qr4 36 10 condition condition NN cord-326740-1fjr9qr4 36 11 and and CC cord-326740-1fjr9qr4 36 12 obtain obtain VB cord-326740-1fjr9qr4 36 13 closed close VBN cord-326740-1fjr9qr4 36 14 form form NN cord-326740-1fjr9qr4 36 15 expressions expression NNS cord-326740-1fjr9qr4 36 16 for for IN cord-326740-1fjr9qr4 36 17 mean mean JJ cord-326740-1fjr9qr4 36 18 queue queue NN cord-326740-1fjr9qr4 36 19 sizes size NNS cord-326740-1fjr9qr4 36 20 and and CC cord-326740-1fjr9qr4 36 21 mean mean VB cord-326740-1fjr9qr4 36 22 waiting waiting NN cord-326740-1fjr9qr4 36 23 times time NNS cord-326740-1fjr9qr4 36 24 . . . cord-326740-1fjr9qr4 37 1 To to TO cord-326740-1fjr9qr4 37 2 address address VB cord-326740-1fjr9qr4 37 3 the the DT cord-326740-1fjr9qr4 37 4 issues issue NNS cord-326740-1fjr9qr4 37 5 of of IN cord-326740-1fjr9qr4 37 6 controlling control VBG cord-326740-1fjr9qr4 37 7 and and CC cord-326740-1fjr9qr4 37 8 managing manage VBG cord-326740-1fjr9qr4 37 9 queue queue NN cord-326740-1fjr9qr4 37 10 sizes size NNS cord-326740-1fjr9qr4 37 11 to to TO cord-326740-1fjr9qr4 37 12 ensure ensure VB cord-326740-1fjr9qr4 37 13 the the DT cord-326740-1fjr9qr4 37 14 safety safety NN cord-326740-1fjr9qr4 37 15 of of IN cord-326740-1fjr9qr4 37 16 customers customer NNS cord-326740-1fjr9qr4 37 17 and and CC cord-326740-1fjr9qr4 37 18 workers worker NNS cord-326740-1fjr9qr4 37 19 while while IN cord-326740-1fjr9qr4 37 20 reducing reduce VBG cord-326740-1fjr9qr4 37 21 a a DT cord-326740-1fjr9qr4 37 22 store store NN cord-326740-1fjr9qr4 37 23 's 's POS cord-326740-1fjr9qr4 37 24 associated associate VBN cord-326740-1fjr9qr4 37 25 costs cost NNS cord-326740-1fjr9qr4 37 26 , , , cord-326740-1fjr9qr4 37 27 we -PRON- PRP cord-326740-1fjr9qr4 37 28 employ employ VBP cord-326740-1fjr9qr4 37 29 a a DT cord-326740-1fjr9qr4 37 30 game game NN cord-326740-1fjr9qr4 37 31 - - HYPH cord-326740-1fjr9qr4 37 32 theoretic theoretic JJ cord-326740-1fjr9qr4 37 33 model model NN cord-326740-1fjr9qr4 37 34 within within IN cord-326740-1fjr9qr4 37 35 the the DT cord-326740-1fjr9qr4 37 36 queueing queueing NN cord-326740-1fjr9qr4 37 37 framework framework NN cord-326740-1fjr9qr4 37 38 to to TO cord-326740-1fjr9qr4 37 39 investigate investigate VB cord-326740-1fjr9qr4 37 40 equilibrium equilibrium NN cord-326740-1fjr9qr4 37 41 strategies strategy NNS cord-326740-1fjr9qr4 37 42 in in IN cord-326740-1fjr9qr4 37 43 terms term NNS cord-326740-1fjr9qr4 37 44 of of IN cord-326740-1fjr9qr4 37 45 capacity capacity NN cord-326740-1fjr9qr4 37 46 and and CC cord-326740-1fjr9qr4 37 47 number number NN cord-326740-1fjr9qr4 37 48 of of IN cord-326740-1fjr9qr4 37 49 servers server NNS cord-326740-1fjr9qr4 37 50 . . . cord-326740-1fjr9qr4 38 1 In in IN cord-326740-1fjr9qr4 38 2 the the DT cord-326740-1fjr9qr4 38 3 game game NN cord-326740-1fjr9qr4 38 4 , , , cord-326740-1fjr9qr4 38 5 the the DT cord-326740-1fjr9qr4 38 6 authority authority NN cord-326740-1fjr9qr4 38 7 chooses choose VBZ cord-326740-1fjr9qr4 38 8 a a DT cord-326740-1fjr9qr4 38 9 maximum maximum JJ cord-326740-1fjr9qr4 38 10 number number NN cord-326740-1fjr9qr4 38 11 of of IN cord-326740-1fjr9qr4 38 12 customers customer NNS cord-326740-1fjr9qr4 38 13 allowed allow VBN cord-326740-1fjr9qr4 38 14 inside inside IN cord-326740-1fjr9qr4 38 15 the the DT cord-326740-1fjr9qr4 38 16 store store NN cord-326740-1fjr9qr4 38 17 at at IN cord-326740-1fjr9qr4 38 18 a a DT cord-326740-1fjr9qr4 38 19 time time NN cord-326740-1fjr9qr4 38 20 to to TO cord-326740-1fjr9qr4 38 21 minimize minimize VB cord-326740-1fjr9qr4 38 22 the the DT cord-326740-1fjr9qr4 38 23 risk risk NN cord-326740-1fjr9qr4 38 24 of of IN cord-326740-1fjr9qr4 38 25 transmission transmission NN cord-326740-1fjr9qr4 38 26 . . . cord-326740-1fjr9qr4 39 1 We -PRON- PRP cord-326740-1fjr9qr4 39 2 propose propose VBP cord-326740-1fjr9qr4 39 3 a a DT cord-326740-1fjr9qr4 39 4 novel novel JJ cord-326740-1fjr9qr4 39 5 measure measure NN cord-326740-1fjr9qr4 39 6 by by IN cord-326740-1fjr9qr4 39 7 which which WDT cord-326740-1fjr9qr4 39 8 to to TO cord-326740-1fjr9qr4 39 9 evaluate evaluate VB cord-326740-1fjr9qr4 39 10 the the DT cord-326740-1fjr9qr4 39 11 risk risk NN cord-326740-1fjr9qr4 39 12 of of IN cord-326740-1fjr9qr4 39 13 infection infection NN cord-326740-1fjr9qr4 39 14 in in IN cord-326740-1fjr9qr4 39 15 this this DT cord-326740-1fjr9qr4 39 16 scenario scenario NN cord-326740-1fjr9qr4 39 17 . . . cord-326740-1fjr9qr4 40 1 When when WRB cord-326740-1fjr9qr4 40 2 L l NN cord-326740-1fjr9qr4 40 3 customers customer NNS cord-326740-1fjr9qr4 40 4 are be VBP cord-326740-1fjr9qr4 40 5 present present JJ cord-326740-1fjr9qr4 40 6 in in IN cord-326740-1fjr9qr4 40 7 the the DT cord-326740-1fjr9qr4 40 8 store store NN cord-326740-1fjr9qr4 40 9 , , , cord-326740-1fjr9qr4 40 10 each each DT cord-326740-1fjr9qr4 40 11 customer customer NN cord-326740-1fjr9qr4 40 12 can can MD cord-326740-1fjr9qr4 40 13 be be VB cord-326740-1fjr9qr4 40 14 infected infect VBN cord-326740-1fjr9qr4 40 15 by by IN cord-326740-1fjr9qr4 40 16 ( ( -LRB- cord-326740-1fjr9qr4 40 17 the the DT cord-326740-1fjr9qr4 40 18 other other JJ cord-326740-1fjr9qr4 40 19 ) ) -RRB- cord-326740-1fjr9qr4 40 20 L l NN cord-326740-1fjr9qr4 40 21 -1 -1 NNP cord-326740-1fjr9qr4 40 22 customers customer NNS cord-326740-1fjr9qr4 40 23 . . . cord-326740-1fjr9qr4 41 1 safety safety NN cord-326740-1fjr9qr4 41 2 problem problem NN cord-326740-1fjr9qr4 41 3 by by IN cord-326740-1fjr9qr4 41 4 developing develop VBG cord-326740-1fjr9qr4 41 5 nonclassical nonclassical JJ cord-326740-1fjr9qr4 41 6 multi multi JJ cord-326740-1fjr9qr4 41 7 - - JJ cord-326740-1fjr9qr4 41 8 server server JJ cord-326740-1fjr9qr4 41 9 queueing queueing NN cord-326740-1fjr9qr4 41 10 models model NNS cord-326740-1fjr9qr4 41 11 involving involve VBG cord-326740-1fjr9qr4 41 12 two two CD cord-326740-1fjr9qr4 41 13 service service NN cord-326740-1fjr9qr4 41 14 phases phase NNS cord-326740-1fjr9qr4 41 15 , , , cord-326740-1fjr9qr4 41 16 a a DT cord-326740-1fjr9qr4 41 17 limit limit NN cord-326740-1fjr9qr4 41 18 on on IN cord-326740-1fjr9qr4 41 19 the the DT cord-326740-1fjr9qr4 41 20 number number NN cord-326740-1fjr9qr4 41 21 of of IN cord-326740-1fjr9qr4 41 22 customers customer NNS cord-326740-1fjr9qr4 41 23 in in IN cord-326740-1fjr9qr4 41 24 each each DT cord-326740-1fjr9qr4 41 25 phase phase NN cord-326740-1fjr9qr4 41 26 , , , cord-326740-1fjr9qr4 41 27 and and CC cord-326740-1fjr9qr4 41 28 internal internal JJ cord-326740-1fjr9qr4 41 29 blocking blocking NN cord-326740-1fjr9qr4 41 30 and and CC cord-326740-1fjr9qr4 41 31 delays delay NNS cord-326740-1fjr9qr4 41 32 . . . cord-326740-1fjr9qr4 42 1 We -PRON- PRP cord-326740-1fjr9qr4 42 2 derive derive VBP cord-326740-1fjr9qr4 42 3 and and CC cord-326740-1fjr9qr4 42 4 interpret interpret VBP cord-326740-1fjr9qr4 42 5 the the DT cord-326740-1fjr9qr4 42 6 corresponding corresponding JJ cord-326740-1fjr9qr4 42 7 stability stability NN cord-326740-1fjr9qr4 42 8 conditions condition NNS cord-326740-1fjr9qr4 42 9 . . . cord-326740-1fjr9qr4 43 1 Second second RB cord-326740-1fjr9qr4 43 2 , , , cord-326740-1fjr9qr4 43 3 we -PRON- PRP cord-326740-1fjr9qr4 43 4 construct construct VBP cord-326740-1fjr9qr4 43 5 a a DT cord-326740-1fjr9qr4 43 6 measure measure NN cord-326740-1fjr9qr4 43 7 to to TO cord-326740-1fjr9qr4 43 8 estimate estimate VB cord-326740-1fjr9qr4 43 9 customers customer NNS cord-326740-1fjr9qr4 43 10 ' ' POS cord-326740-1fjr9qr4 43 11 mean mean JJ cord-326740-1fjr9qr4 43 12 risk risk NN cord-326740-1fjr9qr4 43 13 of of IN cord-326740-1fjr9qr4 43 14 infection infection NN cord-326740-1fjr9qr4 43 15 . . . cord-326740-1fjr9qr4 44 1 The the DT cord-326740-1fjr9qr4 44 2 risk risk NN cord-326740-1fjr9qr4 44 3 is be VBZ cord-326740-1fjr9qr4 44 4 proportional proportional JJ cord-326740-1fjr9qr4 44 5 to to IN cord-326740-1fjr9qr4 44 6 the the DT cord-326740-1fjr9qr4 44 7 second second JJ cord-326740-1fjr9qr4 44 8 factorial factorial JJ cord-326740-1fjr9qr4 44 9 moment moment NN cord-326740-1fjr9qr4 44 10 of of IN cord-326740-1fjr9qr4 44 11 the the DT cord-326740-1fjr9qr4 44 12 number number NN cord-326740-1fjr9qr4 44 13 of of IN cord-326740-1fjr9qr4 44 14 customers customer NNS cord-326740-1fjr9qr4 44 15 occupying occupy VBG cord-326740-1fjr9qr4 44 16 the the DT cord-326740-1fjr9qr4 44 17 space space NN cord-326740-1fjr9qr4 44 18 in in IN cord-326740-1fjr9qr4 44 19 each each DT cord-326740-1fjr9qr4 44 20 phase phase NN cord-326740-1fjr9qr4 44 21 of of IN cord-326740-1fjr9qr4 44 22 the the DT cord-326740-1fjr9qr4 44 23 shopping shopping NN cord-326740-1fjr9qr4 44 24 route route NN cord-326740-1fjr9qr4 44 25 . . . cord-326740-1fjr9qr4 45 1 Third third RB cord-326740-1fjr9qr4 45 2 , , , cord-326740-1fjr9qr4 45 3 within within IN cord-326740-1fjr9qr4 45 4 the the DT cord-326740-1fjr9qr4 45 5 queueing queueing NN cord-326740-1fjr9qr4 45 6 framework framework NN cord-326740-1fjr9qr4 45 7 , , , cord-326740-1fjr9qr4 45 8 we -PRON- PRP cord-326740-1fjr9qr4 45 9 formulate formulate VBP cord-326740-1fjr9qr4 45 10 a a DT cord-326740-1fjr9qr4 45 11 game game NN cord-326740-1fjr9qr4 45 12 - - HYPH cord-326740-1fjr9qr4 45 13 theoretic theoretic JJ cord-326740-1fjr9qr4 45 14 model model NN cord-326740-1fjr9qr4 45 15 to to TO cord-326740-1fjr9qr4 45 16 investigate investigate VB cord-326740-1fjr9qr4 45 17 equilibrium equilibrium NN cord-326740-1fjr9qr4 45 18 strategies strategy NNS cord-326740-1fjr9qr4 45 19 in in IN cord-326740-1fjr9qr4 45 20 terms term NNS cord-326740-1fjr9qr4 45 21 of of IN cord-326740-1fjr9qr4 45 22 capacity capacity NN cord-326740-1fjr9qr4 45 23 and and CC cord-326740-1fjr9qr4 45 24 number number NN cord-326740-1fjr9qr4 45 25 of of IN cord-326740-1fjr9qr4 45 26 servers server NNS cord-326740-1fjr9qr4 45 27 . . . cord-326740-1fjr9qr4 46 1 Insights insight NNS cord-326740-1fjr9qr4 46 2 from from IN cord-326740-1fjr9qr4 46 3 our -PRON- PRP$ cord-326740-1fjr9qr4 46 4 models model NNS cord-326740-1fjr9qr4 46 5 are be VBP cord-326740-1fjr9qr4 46 6 useful useful JJ cord-326740-1fjr9qr4 46 7 to to IN cord-326740-1fjr9qr4 46 8 government government NN cord-326740-1fjr9qr4 46 9 authorities authority NNS cord-326740-1fjr9qr4 46 10 and and CC cord-326740-1fjr9qr4 46 11 businesses business NNS cord-326740-1fjr9qr4 46 12 as as IN cord-326740-1fjr9qr4 46 13 they -PRON- PRP cord-326740-1fjr9qr4 46 14 determine determine VBP cord-326740-1fjr9qr4 46 15 a a DT cord-326740-1fjr9qr4 46 16 safe safe JJ cord-326740-1fjr9qr4 46 17 number number NN cord-326740-1fjr9qr4 46 18 of of IN cord-326740-1fjr9qr4 46 19 customers customer NNS cord-326740-1fjr9qr4 46 20 and and CC cord-326740-1fjr9qr4 46 21 employees employee NNS cord-326740-1fjr9qr4 46 22 while while IN cord-326740-1fjr9qr4 46 23 containing contain VBG cord-326740-1fjr9qr4 46 24 the the DT cord-326740-1fjr9qr4 46 25 associated associate VBN cord-326740-1fjr9qr4 46 26 costs cost NNS cord-326740-1fjr9qr4 46 27 of of IN cord-326740-1fjr9qr4 46 28 restrictions restriction NNS cord-326740-1fjr9qr4 46 29 to to IN cord-326740-1fjr9qr4 46 30 businesses business NNS cord-326740-1fjr9qr4 46 31 . . . cord-326740-1fjr9qr4 47 1 In in IN cord-326740-1fjr9qr4 47 2 the the DT cord-326740-1fjr9qr4 47 3 M M NNP cord-326740-1fjr9qr4 47 4 - - HYPH cord-326740-1fjr9qr4 47 5 model model NN cord-326740-1fjr9qr4 47 6 , , , cord-326740-1fjr9qr4 47 7 customers customer NNS cord-326740-1fjr9qr4 47 8 arrive arrive VBP cord-326740-1fjr9qr4 47 9 at at IN cord-326740-1fjr9qr4 47 10 a a DT cord-326740-1fjr9qr4 47 11 store store NN cord-326740-1fjr9qr4 47 12 such such JJ cord-326740-1fjr9qr4 47 13 as as IN cord-326740-1fjr9qr4 47 14 a a DT cord-326740-1fjr9qr4 47 15 supermarket supermarket NN cord-326740-1fjr9qr4 47 16 or or CC cord-326740-1fjr9qr4 47 17 department department NN cord-326740-1fjr9qr4 47 18 store store NN cord-326740-1fjr9qr4 47 19 according accord VBG cord-326740-1fjr9qr4 47 20 to to IN cord-326740-1fjr9qr4 47 21 a a DT cord-326740-1fjr9qr4 47 22 Poisson Poisson NNP cord-326740-1fjr9qr4 47 23 process process NN cord-326740-1fjr9qr4 47 24 with with IN cord-326740-1fjr9qr4 47 25 rate rate NN cord-326740-1fjr9qr4 47 26 λ λ NN cord-326740-1fjr9qr4 47 27 . . . cord-326740-1fjr9qr4 48 1 The the DT cord-326740-1fjr9qr4 48 2 number number NN cord-326740-1fjr9qr4 48 3 of of IN cord-326740-1fjr9qr4 48 4 cashiers cashier NNS cord-326740-1fjr9qr4 48 5 in in IN cord-326740-1fjr9qr4 48 6 the the DT cord-326740-1fjr9qr4 48 7 store store NN cord-326740-1fjr9qr4 48 8 is be VBZ cord-326740-1fjr9qr4 48 9 , , , cord-326740-1fjr9qr4 48 10 each each DT cord-326740-1fjr9qr4 48 11 with with IN cord-326740-1fjr9qr4 48 12 a a DT cord-326740-1fjr9qr4 48 13 service service NN cord-326740-1fjr9qr4 48 14 1 1 CD cord-326740-1fjr9qr4 48 15 c c NN cord-326740-1fjr9qr4 48 16   NNP cord-326740-1fjr9qr4 48 17 duration duration NN cord-326740-1fjr9qr4 48 18 exponentially exponentially RB cord-326740-1fjr9qr4 48 19 distributed distribute VBN cord-326740-1fjr9qr4 48 20 with with IN cord-326740-1fjr9qr4 48 21 mean mean JJ cord-326740-1fjr9qr4 48 22 1/µ. 1/µ. CD cord-326740-1fjr9qr4 49 1 The the DT cord-326740-1fjr9qr4 49 2 authorities authority NNS cord-326740-1fjr9qr4 49 3 have have VBP cord-326740-1fjr9qr4 49 4 imposed impose VBN cord-326740-1fjr9qr4 49 5 a a DT cord-326740-1fjr9qr4 49 6 limit limit NN cord-326740-1fjr9qr4 49 7 of of IN cord-326740-1fjr9qr4 49 8 M M NNP cord-326740-1fjr9qr4 49 9 ≥ ≥ NNP cord-326740-1fjr9qr4 49 10 c c NNP cord-326740-1fjr9qr4 49 11 on on IN cord-326740-1fjr9qr4 49 12 the the DT cord-326740-1fjr9qr4 49 13 maximum maximum JJ cord-326740-1fjr9qr4 49 14 number number NN cord-326740-1fjr9qr4 49 15 of of IN cord-326740-1fjr9qr4 49 16 customers customer NNS cord-326740-1fjr9qr4 49 17 allowed allow VBN cord-326740-1fjr9qr4 49 18 inside inside IN cord-326740-1fjr9qr4 49 19 the the DT cord-326740-1fjr9qr4 49 20 store store NN cord-326740-1fjr9qr4 49 21 at at IN cord-326740-1fjr9qr4 49 22 one one CD cord-326740-1fjr9qr4 49 23 time time NN cord-326740-1fjr9qr4 49 24 . . . cord-326740-1fjr9qr4 50 1 A a DT cord-326740-1fjr9qr4 50 2 customer customer NN cord-326740-1fjr9qr4 50 3 who who WP cord-326740-1fjr9qr4 50 4 arrives arrive VBZ cord-326740-1fjr9qr4 50 5 when when WRB cord-326740-1fjr9qr4 50 6 there there EX cord-326740-1fjr9qr4 50 7 are be VBP cord-326740-1fjr9qr4 50 8 M M NNP cord-326740-1fjr9qr4 50 9 customers customer NNS cord-326740-1fjr9qr4 50 10 already already RB cord-326740-1fjr9qr4 50 11 in in IN cord-326740-1fjr9qr4 50 12 the the DT cord-326740-1fjr9qr4 50 13 store store NN cord-326740-1fjr9qr4 50 14 must must MD cord-326740-1fjr9qr4 50 15 wait wait VB cord-326740-1fjr9qr4 50 16 outside outside RB cord-326740-1fjr9qr4 50 17 in in IN cord-326740-1fjr9qr4 50 18 a a DT cord-326740-1fjr9qr4 50 19 line line NN cord-326740-1fjr9qr4 50 20 ( ( -LRB- cord-326740-1fjr9qr4 50 21 an an DT cord-326740-1fjr9qr4 50 22 unlimited unlimited JJ cord-326740-1fjr9qr4 50 23 queue queue NN cord-326740-1fjr9qr4 50 24 ) ) -RRB- cord-326740-1fjr9qr4 50 25 until until IN cord-326740-1fjr9qr4 50 26 permitted permit VBN cord-326740-1fjr9qr4 50 27 to to TO cord-326740-1fjr9qr4 50 28 enter enter VB cord-326740-1fjr9qr4 50 29 . . . cord-326740-1fjr9qr4 51 1 After after IN cord-326740-1fjr9qr4 51 2 entering enter VBG cord-326740-1fjr9qr4 51 3 , , , cord-326740-1fjr9qr4 51 4 each each DT cord-326740-1fjr9qr4 51 5 customer customer NN cord-326740-1fjr9qr4 51 6 passes pass VBZ cord-326740-1fjr9qr4 51 7 through through IN cord-326740-1fjr9qr4 51 8 two two CD cord-326740-1fjr9qr4 51 9 " " `` cord-326740-1fjr9qr4 51 10 service service NN cord-326740-1fjr9qr4 51 11 " " '' cord-326740-1fjr9qr4 51 12 phases phase NNS cord-326740-1fjr9qr4 51 13 -shopping -shopping NN cord-326740-1fjr9qr4 51 14 and and CC cord-326740-1fjr9qr4 51 15 payment payment NN cord-326740-1fjr9qr4 51 16 . . . cord-326740-1fjr9qr4 52 1 In in IN cord-326740-1fjr9qr4 52 2 the the DT cord-326740-1fjr9qr4 52 3 first first JJ cord-326740-1fjr9qr4 52 4 phase phase NN cord-326740-1fjr9qr4 52 5 , , , cord-326740-1fjr9qr4 52 6 the the DT cord-326740-1fjr9qr4 52 7 customer customer NN cord-326740-1fjr9qr4 52 8 spends spend VBZ cord-326740-1fjr9qr4 52 9 a a DT cord-326740-1fjr9qr4 52 10 random random JJ cord-326740-1fjr9qr4 52 11 amount amount NN cord-326740-1fjr9qr4 52 12 of of IN cord-326740-1fjr9qr4 52 13 time time NN cord-326740-1fjr9qr4 52 14 exponentially exponentially RB cord-326740-1fjr9qr4 52 15 distributed distribute VBN cord-326740-1fjr9qr4 52 16 with with IN cord-326740-1fjr9qr4 52 17 mean mean JJ cord-326740-1fjr9qr4 52 18 1 1 CD cord-326740-1fjr9qr4 52 19 / / SYM cord-326740-1fjr9qr4 52 20 ξ ξ NNS cord-326740-1fjr9qr4 52 21 . . . cord-326740-1fjr9qr4 53 1 Upon upon IN cord-326740-1fjr9qr4 53 2 completing complete VBG cord-326740-1fjr9qr4 53 3 shopping shopping NN cord-326740-1fjr9qr4 53 4 , , , cord-326740-1fjr9qr4 53 5 the the DT cord-326740-1fjr9qr4 53 6 customer customer NN cord-326740-1fjr9qr4 53 7 proceeds proceed VBZ cord-326740-1fjr9qr4 53 8 to to IN cord-326740-1fjr9qr4 53 9 the the DT cord-326740-1fjr9qr4 53 10 payment payment NN cord-326740-1fjr9qr4 53 11 phase phase NN cord-326740-1fjr9qr4 53 12 and and CC cord-326740-1fjr9qr4 53 13 either either RB cord-326740-1fjr9qr4 53 14 is be VBZ cord-326740-1fjr9qr4 53 15 served serve VBN cord-326740-1fjr9qr4 53 16 immediately immediately RB cord-326740-1fjr9qr4 53 17 by by IN cord-326740-1fjr9qr4 53 18 a a DT cord-326740-1fjr9qr4 53 19 free free JJ cord-326740-1fjr9qr4 53 20 cashier cashier NN cord-326740-1fjr9qr4 53 21 or or CC cord-326740-1fjr9qr4 53 22 waits wait VBZ cord-326740-1fjr9qr4 53 23 in in IN cord-326740-1fjr9qr4 53 24 a a DT cord-326740-1fjr9qr4 53 25 line line NN cord-326740-1fjr9qr4 53 26 forming form VBG cord-326740-1fjr9qr4 53 27 in in IN cord-326740-1fjr9qr4 53 28 front front NN cord-326740-1fjr9qr4 53 29 of of IN cord-326740-1fjr9qr4 53 30 the the DT cord-326740-1fjr9qr4 53 31 cashiers cashier NNS cord-326740-1fjr9qr4 53 32 . . . cord-326740-1fjr9qr4 54 1 Shopping shopping NN cord-326740-1fjr9qr4 54 2 times time NNS cord-326740-1fjr9qr4 54 3 , , , cord-326740-1fjr9qr4 54 4 payment payment NN cord-326740-1fjr9qr4 54 5 times time NNS cord-326740-1fjr9qr4 54 6 , , , cord-326740-1fjr9qr4 54 7 and and CC cord-326740-1fjr9qr4 54 8 the the DT cord-326740-1fjr9qr4 54 9 arrival arrival NN cord-326740-1fjr9qr4 54 10 process process NN cord-326740-1fjr9qr4 54 11 are be VBP cord-326740-1fjr9qr4 54 12 independent independent JJ cord-326740-1fjr9qr4 54 13 . . . cord-326740-1fjr9qr4 55 1 This this DT cord-326740-1fjr9qr4 55 2 two two CD cord-326740-1fjr9qr4 55 3 - - HYPH cord-326740-1fjr9qr4 55 4 phase phase NN cord-326740-1fjr9qr4 55 5 service service NN cord-326740-1fjr9qr4 55 6 process process NN cord-326740-1fjr9qr4 55 7 can can MD cord-326740-1fjr9qr4 55 8 appear appear VB cord-326740-1fjr9qr4 55 9 to to TO cord-326740-1fjr9qr4 55 10 be be VB cord-326740-1fjr9qr4 55 11 a a DT cord-326740-1fjr9qr4 55 12 two two CD cord-326740-1fjr9qr4 55 13 - - HYPH cord-326740-1fjr9qr4 55 14 site site NN cord-326740-1fjr9qr4 55 15 tandem tandem NN cord-326740-1fjr9qr4 55 16 network network NN cord-326740-1fjr9qr4 55 17 ( ( -LRB- cord-326740-1fjr9qr4 55 18 see see UH cord-326740-1fjr9qr4 55 19 , , , cord-326740-1fjr9qr4 55 20 e.g. e.g. RB cord-326740-1fjr9qr4 55 21 , , , cord-326740-1fjr9qr4 55 22 Perlman Perlman NNP cord-326740-1fjr9qr4 55 23 and and CC cord-326740-1fjr9qr4 55 24 Yechiali Yechiali NNP cord-326740-1fjr9qr4 55 25 ( ( -LRB- cord-326740-1fjr9qr4 55 26 2020 2020 CD cord-326740-1fjr9qr4 55 27 ) ) -RRB- cord-326740-1fjr9qr4 55 28 ) ) -RRB- cord-326740-1fjr9qr4 55 29 , , , cord-326740-1fjr9qr4 55 30 but but CC cord-326740-1fjr9qr4 55 31 that that DT cord-326740-1fjr9qr4 55 32 is be VBZ cord-326740-1fjr9qr4 55 33 not not RB cord-326740-1fjr9qr4 55 34 the the DT cord-326740-1fjr9qr4 55 35 case case NN cord-326740-1fjr9qr4 55 36 since since IN cord-326740-1fjr9qr4 55 37 the the DT cord-326740-1fjr9qr4 55 38 two two CD cord-326740-1fjr9qr4 55 39 service service NN cord-326740-1fjr9qr4 55 40 stages stage NNS cord-326740-1fjr9qr4 55 41 are be VBP cord-326740-1fjr9qr4 55 42 dependent dependent JJ cord-326740-1fjr9qr4 55 43 via via IN cord-326740-1fjr9qr4 55 44 the the DT cord-326740-1fjr9qr4 55 45 imposed impose VBN cord-326740-1fjr9qr4 55 46 upper upper JJ cord-326740-1fjr9qr4 55 47 limit limit NN cord-326740-1fjr9qr4 55 48 on on IN cord-326740-1fjr9qr4 55 49 the the DT cord-326740-1fjr9qr4 55 50 total total JJ cord-326740-1fjr9qr4 55 51 number number NN cord-326740-1fjr9qr4 55 52 of of IN cord-326740-1fjr9qr4 55 53 customers customer NNS cord-326740-1fjr9qr4 55 54 allowed allow VBN cord-326740-1fjr9qr4 55 55 inside inside IN cord-326740-1fjr9qr4 55 56 the the DT cord-326740-1fjr9qr4 55 57 store store NN cord-326740-1fjr9qr4 55 58 in in IN cord-326740-1fjr9qr4 55 59 both both DT cord-326740-1fjr9qr4 55 60 phases phase NNS cord-326740-1fjr9qr4 55 61 . . . cord-326740-1fjr9qr4 56 1 In in IN cord-326740-1fjr9qr4 56 2 addition addition NN cord-326740-1fjr9qr4 56 3 , , , cord-326740-1fjr9qr4 56 4 in in IN cord-326740-1fjr9qr4 56 5 the the DT cord-326740-1fjr9qr4 56 6 current current JJ cord-326740-1fjr9qr4 56 7 model model NN cord-326740-1fjr9qr4 56 8 , , , cord-326740-1fjr9qr4 56 9 the the DT cord-326740-1fjr9qr4 56 10 time time NN cord-326740-1fjr9qr4 56 11 deterioration deterioration NN cord-326740-1fjr9qr4 56 12 considered consider VBN cord-326740-1fjr9qr4 56 13 in in IN cord-326740-1fjr9qr4 56 14 Perlman Perlman NNP cord-326740-1fjr9qr4 56 15 and and CC cord-326740-1fjr9qr4 56 16 Yechiali Yechiali NNP cord-326740-1fjr9qr4 56 17 ( ( -LRB- cord-326740-1fjr9qr4 56 18 2020 2020 CD cord-326740-1fjr9qr4 56 19 ) ) -RRB- cord-326740-1fjr9qr4 56 20 is be VBZ cord-326740-1fjr9qr4 56 21 replaced replace VBN cord-326740-1fjr9qr4 56 22 by by IN cord-326740-1fjr9qr4 56 23 the the DT cord-326740-1fjr9qr4 56 24 increased increase VBN cord-326740-1fjr9qr4 56 25 risk risk NN cord-326740-1fjr9qr4 56 26 of of IN cord-326740-1fjr9qr4 56 27 infection infection NN cord-326740-1fjr9qr4 56 28 associated associate VBN cord-326740-1fjr9qr4 56 29 with with IN cord-326740-1fjr9qr4 56 30 customer customer NN cord-326740-1fjr9qr4 56 31 crowding crowding NN cord-326740-1fjr9qr4 56 32 . . . cord-326740-1fjr9qr4 57 1 Let let VB cord-326740-1fjr9qr4 57 2 L L NNP cord-326740-1fjr9qr4 57 3 1 1 CD cord-326740-1fjr9qr4 57 4 denote denote VB cord-326740-1fjr9qr4 57 5 the the DT cord-326740-1fjr9qr4 57 6 number number NN cord-326740-1fjr9qr4 57 7 of of IN cord-326740-1fjr9qr4 57 8 customers customer NNS cord-326740-1fjr9qr4 57 9 either either CC cord-326740-1fjr9qr4 57 10 in in IN cord-326740-1fjr9qr4 57 11 the the DT cord-326740-1fjr9qr4 57 12 shopping shopping NN cord-326740-1fjr9qr4 57 13 phase phase NN cord-326740-1fjr9qr4 57 14 or or CC cord-326740-1fjr9qr4 57 15 waiting wait VBG cord-326740-1fjr9qr4 57 16 outside outside IN cord-326740-1fjr9qr4 57 17 the the DT cord-326740-1fjr9qr4 57 18 store store NN cord-326740-1fjr9qr4 57 19 . . . cord-326740-1fjr9qr4 58 1 Note note VB cord-326740-1fjr9qr4 58 2 that that IN cord-326740-1fjr9qr4 58 3 L l NN cord-326740-1fjr9qr4 58 4 1 1 CD cord-326740-1fjr9qr4 58 5 is be VBZ cord-326740-1fjr9qr4 58 6 unbounded unbounded JJ cord-326740-1fjr9qr4 58 7 ( ( -LRB- cord-326740-1fjr9qr4 58 8 since since IN cord-326740-1fjr9qr4 58 9 we -PRON- PRP cord-326740-1fjr9qr4 58 10 do do VBP cord-326740-1fjr9qr4 58 11 not not RB cord-326740-1fjr9qr4 58 12 restrict restrict VB cord-326740-1fjr9qr4 58 13 the the DT cord-326740-1fjr9qr4 58 14 number number NN cord-326740-1fjr9qr4 58 15 of of IN cord-326740-1fjr9qr4 58 16 customers customer NNS cord-326740-1fjr9qr4 58 17 allowed allow VBN cord-326740-1fjr9qr4 58 18 to to TO cord-326740-1fjr9qr4 58 19 wait wait VB cord-326740-1fjr9qr4 58 20 outside outside RB cord-326740-1fjr9qr4 58 21 ) ) -RRB- cord-326740-1fjr9qr4 58 22 . . . cord-326740-1fjr9qr4 59 1 Let let VB cord-326740-1fjr9qr4 59 2 L l NN cord-326740-1fjr9qr4 59 3 2 2 CD cord-326740-1fjr9qr4 59 4 denote denote VB cord-326740-1fjr9qr4 59 5 the the DT cord-326740-1fjr9qr4 59 6 number number NN cord-326740-1fjr9qr4 59 7 of of IN cord-326740-1fjr9qr4 59 8 customers customer NNS cord-326740-1fjr9qr4 59 9 in in IN cord-326740-1fjr9qr4 59 10 the the DT cord-326740-1fjr9qr4 59 11 payment payment NN cord-326740-1fjr9qr4 59 12 phase phase NN cord-326740-1fjr9qr4 59 13 who who WP cord-326740-1fjr9qr4 59 14 are be VBP cord-326740-1fjr9qr4 59 15 either either DT cord-326740-1fjr9qr4 59 16 being be VBG cord-326740-1fjr9qr4 59 17 served serve VBN cord-326740-1fjr9qr4 59 18 by by IN cord-326740-1fjr9qr4 59 19 a a DT cord-326740-1fjr9qr4 59 20 cashier cashier NN cord-326740-1fjr9qr4 59 21 or or CC cord-326740-1fjr9qr4 59 22 are be VBP cord-326740-1fjr9qr4 59 23 waiting wait VBG cord-326740-1fjr9qr4 59 24 in in IN cord-326740-1fjr9qr4 59 25 line line NN cord-326740-1fjr9qr4 59 26 for for IN cord-326740-1fjr9qr4 59 27 a a DT cord-326740-1fjr9qr4 59 28 free free JJ cord-326740-1fjr9qr4 59 29 cashier cashier NN cord-326740-1fjr9qr4 59 30 . . . cord-326740-1fjr9qr4 60 1 The the DT cord-326740-1fjr9qr4 60 2 system system NN cord-326740-1fjr9qr4 60 3 can can MD cord-326740-1fjr9qr4 60 4 be be VB cord-326740-1fjr9qr4 60 5 formulated formulate VBN cord-326740-1fjr9qr4 60 6 as as IN cord-326740-1fjr9qr4 60 7 a a DT cord-326740-1fjr9qr4 60 8 two two CD cord-326740-1fjr9qr4 60 9 - - HYPH cord-326740-1fjr9qr4 60 10 dimensional dimensional JJ cord-326740-1fjr9qr4 60 11 quality quality NN cord-326740-1fjr9qr4 60 12 - - HYPH cord-326740-1fjr9qr4 60 13 by by IN cord-326740-1fjr9qr4 60 14 - - HYPH cord-326740-1fjr9qr4 60 15 design design NN cord-326740-1fjr9qr4 60 16 process process NN cord-326740-1fjr9qr4 60 17 with with IN cord-326740-1fjr9qr4 60 18 a a DT cord-326740-1fjr9qr4 60 19 state state NN cord-326740-1fjr9qr4 60 20 - - HYPH cord-326740-1fjr9qr4 60 21 space space NN cord-326740-1fjr9qr4 60 22 of of IN cord-326740-1fjr9qr4 60 23   NNP cord-326740-1fjr9qr4 61 1   NNP cord-326740-1fjr9qr4 61 2 _SP cord-326740-1fjr9qr4 61 3 customers customer NNS cord-326740-1fjr9qr4 61 4 in in IN cord-326740-1fjr9qr4 61 5 the the DT cord-326740-1fjr9qr4 61 6 shopping shopping NN cord-326740-1fjr9qr4 61 7 phase phase NN cord-326740-1fjr9qr4 61 8 . . . cord-326740-1fjr9qr4 62 1 Figure figure NN cord-326740-1fjr9qr4 62 2 1 1 CD cord-326740-1fjr9qr4 62 3 presents present VBZ cord-326740-1fjr9qr4 62 4 a a DT cord-326740-1fjr9qr4 62 5 transition transition NN cord-326740-1fjr9qr4 62 6 - - HYPH cord-326740-1fjr9qr4 62 7 rate rate NN cord-326740-1fjr9qr4 62 8 diagram diagram NN cord-326740-1fjr9qr4 62 9 of of IN cord-326740-1fjr9qr4 62 10 the the DT cord-326740-1fjr9qr4 62 11 M M NNP cord-326740-1fjr9qr4 62 12 - - HYPH cord-326740-1fjr9qr4 62 13 model model NN cord-326740-1fjr9qr4 62 14 system system NN cord-326740-1fjr9qr4 62 15 . . . cord-326740-1fjr9qr4 62 16 _SP cord-326740-1fjr9qr4 63 1 where where WRB cord-326740-1fjr9qr4 63 2 Q Q NNP cord-326740-1fjr9qr4 63 3 is be VBZ cord-326740-1fjr9qr4 63 4 the the DT cord-326740-1fjr9qr4 63 5 so so RB cord-326740-1fjr9qr4 63 6 - - HYPH cord-326740-1fjr9qr4 63 7 called call VBN cord-326740-1fjr9qr4 63 8 infinitesimal infinitesimal JJ cord-326740-1fjr9qr4 63 9 generator generator NN cord-326740-1fjr9qr4 63 10 matrix matrix NN cord-326740-1fjr9qr4 63 11 , , , cord-326740-1fjr9qr4 63 12 is be VBZ cord-326740-1fjr9qr4 63 13 a a DT cord-326740-1fjr9qr4 63 14 row row NN cord-326740-1fjr9qr4 63 15 vector vector NN cord-326740-1fjr9qr4 63 16 of of IN cord-326740-1fjr9qr4 63 17 zeros zero NNS cord-326740-1fjr9qr4 63 18 , , , cord-326740-1fjr9qr4 63 19 and and CC cord-326740-1fjr9qr4 63 20 is be VBZ cord-326740-1fjr9qr4 63 21 a a DT cord-326740-1fjr9qr4 63 22 0 0 CD cord-326740-1fjr9qr4 63 23 e e NN cord-326740-1fjr9qr4 63 24 column column NN cord-326740-1fjr9qr4 63 25 vector vector NN cord-326740-1fjr9qr4 63 26 of of IN cord-326740-1fjr9qr4 63 27 ones one NNS cord-326740-1fjr9qr4 63 28 . . . cord-326740-1fjr9qr4 64 1 The the DT cord-326740-1fjr9qr4 64 2 generator generator NN cord-326740-1fjr9qr4 64 3 matrix matrix NN cord-326740-1fjr9qr4 64 4 Q Q NNP cord-326740-1fjr9qr4 64 5 is be VBZ cord-326740-1fjr9qr4 64 6 given give VBN cord-326740-1fjr9qr4 64 7 by by IN cord-326740-1fjr9qr4 64 8 _SP cord-326740-1fjr9qr4 64 9 where where WRB cord-326740-1fjr9qr4 64 10 is be VBZ cord-326740-1fjr9qr4 64 11 the the DT cord-326740-1fjr9qr4 64 12 element element NN cord-326740-1fjr9qr4 64 13 in in IN cord-326740-1fjr9qr4 64 14 column column NN cord-326740-1fjr9qr4 64 15 n n NN cord-326740-1fjr9qr4 64 16 and and CC cord-326740-1fjr9qr4 64 17 row row NN cord-326740-1fjr9qr4 64 18 k. k. NNP cord-326740-1fjr9qr4 64 19 _SP cord-326740-1fjr9qr4 65 1 all all DT cord-326740-1fjr9qr4 65 2 other other JJ cord-326740-1fjr9qr4 65 3 elements element NNS cord-326740-1fjr9qr4 65 4 equal equal VBP cord-326740-1fjr9qr4 65 5 zero zero CD cord-326740-1fjr9qr4 65 6 ; ; : cord-326740-1fjr9qr4 65 7 … … NFP cord-326740-1fjr9qr4 65 8 … … NFP cord-326740-1fjr9qr4 65 9 and and CC cord-326740-1fjr9qr4 65 10 The the DT cord-326740-1fjr9qr4 65 11 matrices matrix NNS cord-326740-1fjr9qr4 65 12 A a DT cord-326740-1fjr9qr4 65 13 0 0 CD cord-326740-1fjr9qr4 65 14 , , , cord-326740-1fjr9qr4 65 15 A a DT cord-326740-1fjr9qr4 65 16 1 1 CD cord-326740-1fjr9qr4 65 17 , , , cord-326740-1fjr9qr4 65 18 and and CC cord-326740-1fjr9qr4 65 19 A a DT cord-326740-1fjr9qr4 65 20 2 2 CD cord-326740-1fjr9qr4 65 21 are be VBP cord-326740-1fjr9qr4 65 22 square square JJ cord-326740-1fjr9qr4 65 23 matrices matrix NNS cord-326740-1fjr9qr4 65 24 of of IN cord-326740-1fjr9qr4 65 25 order order NN cord-326740-1fjr9qr4 65 26 ( ( -LRB- cord-326740-1fjr9qr4 65 27 M M NNP cord-326740-1fjr9qr4 65 28 + + SYM cord-326740-1fjr9qr4 65 29 1 1 CD cord-326740-1fjr9qr4 65 30 ) ) -RRB- cord-326740-1fjr9qr4 65 31 as as IN cord-326740-1fjr9qr4 65 32 follows follow VBZ cord-326740-1fjr9qr4 65 33 : : : cord-326740-1fjr9qr4 66 1 Matrix Matrix NNP cord-326740-1fjr9qr4 66 2 A A NNP cord-326740-1fjr9qr4 66 3 defines define VBZ cord-326740-1fjr9qr4 66 4 the the DT cord-326740-1fjr9qr4 66 5 underlying underlying JJ cord-326740-1fjr9qr4 66 6 process process NN cord-326740-1fjr9qr4 66 7 of of IN cord-326740-1fjr9qr4 66 8 the the DT cord-326740-1fjr9qr4 66 9 system system NN cord-326740-1fjr9qr4 66 10 , , , cord-326740-1fjr9qr4 66 11 which which WDT cord-326740-1fjr9qr4 66 12 is be VBZ cord-326740-1fjr9qr4 66 13 depicted depict VBN cord-326740-1fjr9qr4 66 14 in in IN cord-326740-1fjr9qr4 66 15 Figure figure NN cord-326740-1fjr9qr4 66 16 2 2 CD cord-326740-1fjr9qr4 66 17 as as IN cord-326740-1fjr9qr4 66 18 a a DT cord-326740-1fjr9qr4 66 19 linear linear JJ cord-326740-1fjr9qr4 66 20 Markov Markov NNP cord-326740-1fjr9qr4 66 21 process process NN cord-326740-1fjr9qr4 66 22 with with IN cord-326740-1fjr9qr4 66 23 M M NNP cord-326740-1fjr9qr4 66 24 + + SYM cord-326740-1fjr9qr4 66 25 1 1 CD cord-326740-1fjr9qr4 66 26 states state NNS cord-326740-1fjr9qr4 66 27 . . . cord-326740-1fjr9qr4 67 1 In in IN cord-326740-1fjr9qr4 67 2 fact fact NN cord-326740-1fjr9qr4 67 3 , , , cord-326740-1fjr9qr4 67 4 the the DT cord-326740-1fjr9qr4 67 5 process process NN cord-326740-1fjr9qr4 67 6 defined define VBN cord-326740-1fjr9qr4 67 7 by by IN cord-326740-1fjr9qr4 67 8 A a DT cord-326740-1fjr9qr4 67 9 can can MD cord-326740-1fjr9qr4 67 10 be be VB cord-326740-1fjr9qr4 67 11 considered consider VBN cord-326740-1fjr9qr4 67 12 as as IN cord-326740-1fjr9qr4 67 13 a a DT cord-326740-1fjr9qr4 67 14 machine machine NN cord-326740-1fjr9qr4 67 15 repair repair NN cord-326740-1fjr9qr4 67 16 problem problem NN cord-326740-1fjr9qr4 67 17 in in IN cord-326740-1fjr9qr4 67 18 which which WDT cord-326740-1fjr9qr4 67 19 repairmen repairman NNS cord-326740-1fjr9qr4 67 20 maintain maintain VBP cord-326740-1fjr9qr4 67 21 machines machine NNS cord-326740-1fjr9qr4 67 22 . . . cord-326740-1fjr9qr4 68 1 The the DT cord-326740-1fjr9qr4 68 2 lifetime lifetime NN cord-326740-1fjr9qr4 68 3 of of IN cord-326740-1fjr9qr4 68 4 1 1 CD cord-326740-1fjr9qr4 68 5 c c NN cord-326740-1fjr9qr4 68 6   NNP cord-326740-1fjr9qr4 68 7 M M NNP cord-326740-1fjr9qr4 68 8 c c NN cord-326740-1fjr9qr4 68 9   NNP cord-326740-1fjr9qr4 68 10 each each DT cord-326740-1fjr9qr4 68 11 machine machine NN cord-326740-1fjr9qr4 68 12 is be VBZ cord-326740-1fjr9qr4 68 13 exponentially exponentially RB cord-326740-1fjr9qr4 68 14 distributed distribute VBN cord-326740-1fjr9qr4 68 15 with with IN cord-326740-1fjr9qr4 68 16 parameter parameter NN cord-326740-1fjr9qr4 68 17 and and CC cord-326740-1fjr9qr4 68 18 the the DT cord-326740-1fjr9qr4 68 19 repair repair NN cord-326740-1fjr9qr4 68 20 time time NN cord-326740-1fjr9qr4 68 21 of of IN cord-326740-1fjr9qr4 68 22 a a DT cord-326740-1fjr9qr4 68 23 machine machine NN cord-326740-1fjr9qr4 68 24 by by IN cord-326740-1fjr9qr4 68 25 a a DT cord-326740-1fjr9qr4 68 26   NNP cord-326740-1fjr9qr4 68 27 repairman repairman NN cord-326740-1fjr9qr4 68 28 is be VBZ cord-326740-1fjr9qr4 68 29 exponential exponential JJ cord-326740-1fjr9qr4 68 30 with with IN cord-326740-1fjr9qr4 68 31 intensity intensity NN cord-326740-1fjr9qr4 68 32 . . . cord-326740-1fjr9qr4 69 1 The the DT cord-326740-1fjr9qr4 69 2 state state NN cord-326740-1fjr9qr4 69 3 of of IN cord-326740-1fjr9qr4 69 4 the the DT cord-326740-1fjr9qr4 69 5 system system NN cord-326740-1fjr9qr4 69 6 is be VBZ cord-326740-1fjr9qr4 69 7 the the DT cord-326740-1fjr9qr4 69 8 number number NN cord-326740-1fjr9qr4 69 9 of of IN cord-326740-1fjr9qr4 69 10 unbroken unbroken JJ cord-326740-1fjr9qr4 69 11 μ μ NN cord-326740-1fjr9qr4 69 12 machines machine NNS cord-326740-1fjr9qr4 69 13 . . . cord-326740-1fjr9qr4 70 1 Denote denote VB cord-326740-1fjr9qr4 70 2 by by IN cord-326740-1fjr9qr4 70 3 the the DT cord-326740-1fjr9qr4 70 4 stationary stationary JJ cord-326740-1fjr9qr4 70 5 probability probability NN cord-326740-1fjr9qr4 70 6 vector vector NN cord-326740-1fjr9qr4 70 7 satisfying satisfying NN cord-326740-1fjr9qr4 70 8 and and CC cord-326740-1fjr9qr4 70 9 0 0 CD cord-326740-1fjr9qr4 70 10 1 1 CD cord-326740-1fjr9qr4 70 11 ( ( -LRB- cord-326740-1fjr9qr4 70 12 , , , cord-326740-1fjr9qr4 70 13 , , , cord-326740-1fjr9qr4 70 14 ... ... NFP cord-326740-1fjr9qr4 70 15 , , , cord-326740-1fjr9qr4 70 16 ) ) -RRB- cord-326740-1fjr9qr4 71 1 The the DT cord-326740-1fjr9qr4 71 2 system system NN cord-326740-1fjr9qr4 71 3 stability stability NN cord-326740-1fjr9qr4 71 4 condition condition NN cord-326740-1fjr9qr4 71 5 ( ( -LRB- cord-326740-1fjr9qr4 71 6 Neuts Neuts NNPS cord-326740-1fjr9qr4 71 7 , , , cord-326740-1fjr9qr4 71 8 1981 1981 CD cord-326740-1fjr9qr4 71 9 ) ) -RRB- cord-326740-1fjr9qr4 71 10 is be VBZ cord-326740-1fjr9qr4 71 11 , , , cord-326740-1fjr9qr4 71 12 and and CC cord-326740-1fjr9qr4 71 13 the the DT cord-326740-1fjr9qr4 71 14 system system NN cord-326740-1fjr9qr4 71 15 is be VBZ cord-326740-1fjr9qr4 71 16 stable stable JJ cord-326740-1fjr9qr4 71 17 if if IN cord-326740-1fjr9qr4 72 1 and and CC cord-326740-1fjr9qr4 72 2 Next Next NNP cord-326740-1fjr9qr4 72 3 , , , cord-326740-1fjr9qr4 72 4 we -PRON- PRP cord-326740-1fjr9qr4 72 5 explore explore VBP cord-326740-1fjr9qr4 72 6 the the DT cord-326740-1fjr9qr4 72 7 stability stability NN cord-326740-1fjr9qr4 72 8 condition condition NN cord-326740-1fjr9qr4 72 9 stated state VBN cord-326740-1fjr9qr4 72 10 in in IN cord-326740-1fjr9qr4 72 11 Proposition Proposition NNP cord-326740-1fjr9qr4 72 12 1 1 CD cord-326740-1fjr9qr4 72 13 and and CC cord-326740-1fjr9qr4 72 14 provide provide VB cord-326740-1fjr9qr4 72 15 intuition intuition NN cord-326740-1fjr9qr4 72 16 for for IN cord-326740-1fjr9qr4 72 17 the the DT cord-326740-1fjr9qr4 72 18 results result NNS cord-326740-1fjr9qr4 72 19 . . . cord-326740-1fjr9qr4 73 1 In in IN cord-326740-1fjr9qr4 73 2 particular particular JJ cord-326740-1fjr9qr4 73 3 , , , cord-326740-1fjr9qr4 73 4 the the DT cord-326740-1fjr9qr4 73 5 righthand righthand JJ cord-326740-1fjr9qr4 73 6 side side NN cord-326740-1fjr9qr4 73 7 of of IN cord-326740-1fjr9qr4 73 8 the the DT cord-326740-1fjr9qr4 73 9 stability stability NN cord-326740-1fjr9qr4 73 10 condition condition NN cord-326740-1fjr9qr4 73 11 approaches approach VBZ cord-326740-1fjr9qr4 73 12 as as IN cord-326740-1fjr9qr4 73 13 μ μ NN cord-326740-1fjr9qr4 73 14 c c NNP cord-326740-1fjr9qr4 73 15   NNP cord-326740-1fjr9qr4 73 16 approaches approach VBZ cord-326740-1fjr9qr4 73 17 infinity infinity NN cord-326740-1fjr9qr4 73 18 , , , cord-326740-1fjr9qr4 73 19 and and CC cord-326740-1fjr9qr4 73 20 the the DT cord-326740-1fjr9qr4 73 21 system system NN cord-326740-1fjr9qr4 73 22 then then RB cord-326740-1fjr9qr4 73 23 becomes become VBZ cord-326740-1fjr9qr4 73 24 Erlang Erlang NNP cord-326740-1fjr9qr4 73 25 's 's POS cord-326740-1fjr9qr4 73 26 delay delay NN cord-326740-1fjr9qr4 73 27 queue queue NN cord-326740-1fjr9qr4 73 28 : : : cord-326740-1fjr9qr4 73 29 an an DT cord-326740-1fjr9qr4 73 30 M(λ m(λ NN cord-326740-1fjr9qr4 73 31 ) ) -RRB- cord-326740-1fjr9qr4 73 32 / / . cord-326740-1fjr9qr4 74 1 M M NNP cord-326740-1fjr9qr4 74 2 ( ( -LRB- cord-326740-1fjr9qr4 75 1 ) ) -RRB- cord-326740-1fjr9qr4 75 2 / / SYM cord-326740-1fjr9qr4 75 3 c c NN cord-326740-1fjr9qr4 75 4 queue queue NN cord-326740-1fjr9qr4 75 5 μ μ NN cord-326740-1fjr9qr4 75 6 with with IN cord-326740-1fjr9qr4 75 7 arrival arrival NN cord-326740-1fjr9qr4 75 8 rate rate NN cord-326740-1fjr9qr4 75 9 λ λ NN cord-326740-1fjr9qr4 75 10 and and CC cord-326740-1fjr9qr4 75 11 c c LS cord-326740-1fjr9qr4 75 12 parallel parallel NN cord-326740-1fjr9qr4 75 13 servers server NNS cord-326740-1fjr9qr4 75 14 who who WP cord-326740-1fjr9qr4 75 15 each each DT cord-326740-1fjr9qr4 75 16 serve serve VBP cord-326740-1fjr9qr4 75 17 at at IN cord-326740-1fjr9qr4 75 18 rate rate NN cord-326740-1fjr9qr4 75 19 . . . cord-326740-1fjr9qr4 76 1 The the DT cord-326740-1fjr9qr4 76 2 stability stability NN cord-326740-1fjr9qr4 76 3 condition condition NN cord-326740-1fjr9qr4 76 4 is be VBZ cord-326740-1fjr9qr4 76 5 then then RB cord-326740-1fjr9qr4 76 6 μ μ NN cord-326740-1fjr9qr4 76 7 λ λ NN cord-326740-1fjr9qr4 76 8 μ μ NN cord-326740-1fjr9qr4 76 9 . . . cord-326740-1fjr9qr4 77 1 c c NNP cord-326740-1fjr9qr4 77 2   NNP cord-326740-1fjr9qr4 78 1 As as IN cord-326740-1fjr9qr4 78 2 approaches approach VBZ cord-326740-1fjr9qr4 78 3 infinity infinity NN cord-326740-1fjr9qr4 78 4 , , , cord-326740-1fjr9qr4 78 5 the the DT cord-326740-1fjr9qr4 78 6 mean mean JJ cord-326740-1fjr9qr4 78 7 total total JJ cord-326740-1fjr9qr4 78 8 service service NN cord-326740-1fjr9qr4 78 9 time time NN cord-326740-1fjr9qr4 78 10 for for IN cord-326740-1fjr9qr4 78 11 each each DT cord-326740-1fjr9qr4 78 12 costumer costumer NN cord-326740-1fjr9qr4 78 13 is be VBZ cord-326740-1fjr9qr4 78 14 so so RB cord-326740-1fjr9qr4 78 15 the the DT cord-326740-1fjr9qr4 78 16 μ μ NN cord-326740-1fjr9qr4 78 17 1 1 CD cord-326740-1fjr9qr4 78 18 / / SYM cord-326740-1fjr9qr4 78 19   NNP cord-326740-1fjr9qr4 78 20 system system NN cord-326740-1fjr9qr4 78 21 becomes become VBZ cord-326740-1fjr9qr4 78 22 an an DT cord-326740-1fjr9qr4 78 23 Erlang Erlang NNP cord-326740-1fjr9qr4 78 24 's 's POS cord-326740-1fjr9qr4 78 25 delay delay NN cord-326740-1fjr9qr4 78 26 queue queue NN cord-326740-1fjr9qr4 78 27 with with IN cord-326740-1fjr9qr4 78 28 parallel parallel JJ cord-326740-1fjr9qr4 78 29 servers server NNS cord-326740-1fjr9qr4 78 30 and and CC cord-326740-1fjr9qr4 78 31 the the DT cord-326740-1fjr9qr4 78 32 stability stability NN cord-326740-1fjr9qr4 78 33 condition condition NN cord-326740-1fjr9qr4 78 34 is be VBZ cord-326740-1fjr9qr4 78 35 M M NNP cord-326740-1fjr9qr4 78 36 Similarly similarly RB cord-326740-1fjr9qr4 78 37 , , , cord-326740-1fjr9qr4 78 38 when when WRB cord-326740-1fjr9qr4 78 39 M M NNP cord-326740-1fjr9qr4 78 40 approaches approach VBZ cord-326740-1fjr9qr4 78 41 infinity infinity NN cord-326740-1fjr9qr4 78 42 , , , cord-326740-1fjr9qr4 78 43 the the DT cord-326740-1fjr9qr4 78 44 shopping shopping NN cord-326740-1fjr9qr4 78 45 phase phase NN cord-326740-1fjr9qr4 78 46 becomes become VBZ cord-326740-1fjr9qr4 78 47 an an DT cord-326740-1fjr9qr4 78 48 M(λ m(λ NN cord-326740-1fjr9qr4 78 49 ) ) -RRB- cord-326740-1fjr9qr4 79 1 / / SYM cord-326740-1fjr9qr4 79 2 M M NNP cord-326740-1fjr9qr4 79 3 ( ( -LRB- cord-326740-1fjr9qr4 79 4 ) ) -RRB- cord-326740-1fjr9qr4 79 5 / / NFP cord-326740-1fjr9qr4 79 6   NNP cord-326740-1fjr9qr4 79 7   NN cord-326740-1fjr9qr4 79 8 queue queue NN cord-326740-1fjr9qr4 79 9 with with IN cord-326740-1fjr9qr4 79 10 an an DT cord-326740-1fjr9qr4 79 11 output output NN cord-326740-1fjr9qr4 79 12 Poisson Poisson NNP cord-326740-1fjr9qr4 79 13 process process NN cord-326740-1fjr9qr4 79 14 ( ( -LRB- cord-326740-1fjr9qr4 79 15 λ λ NN cord-326740-1fjr9qr4 79 16 ) ) -RRB- cord-326740-1fjr9qr4 79 17 . . . cord-326740-1fjr9qr4 80 1 Therefore therefore RB cord-326740-1fjr9qr4 80 2 , , , cord-326740-1fjr9qr4 80 3 the the DT cord-326740-1fjr9qr4 80 4 payment payment NN cord-326740-1fjr9qr4 80 5 phase phase NN cord-326740-1fjr9qr4 80 6 becomes become VBZ cord-326740-1fjr9qr4 80 7 an an DT cord-326740-1fjr9qr4 80 8 _SP cord-326740-1fjr9qr4 80 9 server server NN cord-326740-1fjr9qr4 80 10 ( ( -LRB- cord-326740-1fjr9qr4 80 11 cashier cashier NN cord-326740-1fjr9qr4 80 12 ) ) -RRB- cord-326740-1fjr9qr4 80 13 , , , cord-326740-1fjr9qr4 80 14 the the DT cord-326740-1fjr9qr4 80 15 right right JJ cord-326740-1fjr9qr4 80 16 - - HYPH cord-326740-1fjr9qr4 80 17 hand hand NN cord-326740-1fjr9qr4 80 18 side side NN cord-326740-1fjr9qr4 80 19 of of IN cord-326740-1fjr9qr4 80 20 the the DT cord-326740-1fjr9qr4 80 21 stability stability NN cord-326740-1fjr9qr4 80 22 condition condition NN cord-326740-1fjr9qr4 80 23 equals equal VBZ cord-326740-1fjr9qr4 80 24 where where WRB cord-326740-1fjr9qr4 80 25 is be VBZ cord-326740-1fjr9qr4 80 26 the the DT cord-326740-1fjr9qr4 80 27 incomplete incomplete JJ cord-326740-1fjr9qr4 80 28 Gamma Gamma NNP cord-326740-1fjr9qr4 80 29 function function NN cord-326740-1fjr9qr4 80 30 . . . cord-326740-1fjr9qr4 81 1 ( ( -LRB- cord-326740-1fjr9qr4 81 2 1 1 LS cord-326740-1fjr9qr4 81 3 ) ) -RRB- cord-326740-1fjr9qr4 81 4 As as IN cord-326740-1fjr9qr4 81 5 in in IN cord-326740-1fjr9qr4 81 6 Neuts Neuts NNPS cord-326740-1fjr9qr4 81 7 ( ( -LRB- cord-326740-1fjr9qr4 81 8 1981 1981 CD cord-326740-1fjr9qr4 81 9 ) ) -RRB- cord-326740-1fjr9qr4 81 10 , , , cord-326740-1fjr9qr4 81 11 a a DT cord-326740-1fjr9qr4 81 12 rate rate NN cord-326740-1fjr9qr4 81 13 matrix matrix NN cord-326740-1fjr9qr4 81 14 R r NN cord-326740-1fjr9qr4 81 15 exists exist VBZ cord-326740-1fjr9qr4 81 16 that that IN cord-326740-1fjr9qr4 81 17 satisfies satisfie NNS cord-326740-1fjr9qr4 81 18 in in IN cord-326740-1fjr9qr4 81 19 which which WDT cord-326740-1fjr9qr4 81 20 the the DT cord-326740-1fjr9qr4 81 21 probability probability NN cord-326740-1fjr9qr4 81 22 vectors vector NNS cord-326740-1fjr9qr4 81 23 satisfy satisfy VBP cord-326740-1fjr9qr4 81 24 R r NN cord-326740-1fjr9qr4 81 25 is be VBZ cord-326740-1fjr9qr4 81 26 the the DT cord-326740-1fjr9qr4 81 27 minimal minimal JJ cord-326740-1fjr9qr4 81 28 non non JJ cord-326740-1fjr9qr4 81 29 - - JJ cord-326740-1fjr9qr4 81 30 negative negative JJ cord-326740-1fjr9qr4 81 31 solution solution NN cord-326740-1fjr9qr4 81 32 of of IN cord-326740-1fjr9qr4 81 33 equation equation NN cord-326740-1fjr9qr4 81 34 3 3 CD cord-326740-1fjr9qr4 81 35 and and CC cord-326740-1fjr9qr4 81 36 is be VBZ cord-326740-1fjr9qr4 81 37 usually usually RB cord-326740-1fjr9qr4 81 38 calculated calculate VBN cord-326740-1fjr9qr4 81 39 numerically numerically RB cord-326740-1fjr9qr4 81 40 via via IN cord-326740-1fjr9qr4 81 41 a a DT cord-326740-1fjr9qr4 81 42 successive successive JJ cord-326740-1fjr9qr4 81 43 substitution substitution NN cord-326740-1fjr9qr4 81 44 algorithm algorithm NN cord-326740-1fjr9qr4 81 45 ( ( -LRB- cord-326740-1fjr9qr4 81 46 see see UH cord-326740-1fjr9qr4 81 47 , , , cord-326740-1fjr9qr4 81 48 e.g. e.g. RB cord-326740-1fjr9qr4 81 49 , , , cord-326740-1fjr9qr4 81 50 Harchol Harchol NNP cord-326740-1fjr9qr4 81 51 - - HYPH cord-326740-1fjr9qr4 81 52 Balter Balter NNP cord-326740-1fjr9qr4 81 53 ( ( -LRB- cord-326740-1fjr9qr4 81 54 2013 2013 CD cord-326740-1fjr9qr4 81 55 ) ) -RRB- cord-326740-1fjr9qr4 81 56 ) ) -RRB- cord-326740-1fjr9qr4 81 57 . . . cord-326740-1fjr9qr4 82 1 See see VB cord-326740-1fjr9qr4 82 2 Hanukov Hanukov NNP cord-326740-1fjr9qr4 82 3 and and CC cord-326740-1fjr9qr4 82 4 Yechiali Yechiali NNP cord-326740-1fjr9qr4 82 5 ( ( -LRB- cord-326740-1fjr9qr4 82 6 2020 2020 CD cord-326740-1fjr9qr4 82 7 ) ) -RRB- cord-326740-1fjr9qr4 82 8 for for IN cord-326740-1fjr9qr4 82 9 cases case NNS cord-326740-1fjr9qr4 82 10 in in IN cord-326740-1fjr9qr4 82 11 which which WDT cord-326740-1fjr9qr4 82 12 matrix matrix NN cord-326740-1fjr9qr4 82 13 R r NN cord-326740-1fjr9qr4 82 14 can can MD cord-326740-1fjr9qr4 82 15 be be VB cord-326740-1fjr9qr4 82 16 expressed express VBN cord-326740-1fjr9qr4 82 17 explicitly explicitly RB cord-326740-1fjr9qr4 82 18 . . . cord-326740-1fjr9qr4 83 1 By by IN cord-326740-1fjr9qr4 83 2 equations equation NNS cord-326740-1fjr9qr4 83 3 1 1 CD cord-326740-1fjr9qr4 83 4 and and CC cord-326740-1fjr9qr4 83 5 2 2 CD cord-326740-1fjr9qr4 83 6 , , , cord-326740-1fjr9qr4 83 7 the the DT cord-326740-1fjr9qr4 83 8 balance balance NN cord-326740-1fjr9qr4 83 9 equations equation NNS cord-326740-1fjr9qr4 83 10 are be VBP cord-326740-1fjr9qr4 83 11 The the DT cord-326740-1fjr9qr4 83 12 equations equation NNS cord-326740-1fjr9qr4 83 13 5 5 CD cord-326740-1fjr9qr4 83 14 , , , cord-326740-1fjr9qr4 83 15 6 6 CD cord-326740-1fjr9qr4 83 16 , , , cord-326740-1fjr9qr4 83 17 and and CC cord-326740-1fjr9qr4 83 18 7 7 CD cord-326740-1fjr9qr4 83 19 uniquely uniquely RB cord-326740-1fjr9qr4 83 20 determine determine VBP cord-326740-1fjr9qr4 83 21 the the DT cord-326740-1fjr9qr4 83 22 boundary boundary JJ cord-326740-1fjr9qr4 83 23 probability probability NN cord-326740-1fjr9qr4 83 24 vectors vector NNS cord-326740-1fjr9qr4 83 25 _SP cord-326740-1fjr9qr4 83 26 Since since IN cord-326740-1fjr9qr4 83 27 the the DT cord-326740-1fjr9qr4 83 28 risk risk NN cord-326740-1fjr9qr4 83 29 of of IN cord-326740-1fjr9qr4 83 30 infection infection NN cord-326740-1fjr9qr4 83 31 increases increase VBZ cord-326740-1fjr9qr4 83 32 as as IN cord-326740-1fjr9qr4 83 33 the the DT cord-326740-1fjr9qr4 83 34 number number NN cord-326740-1fjr9qr4 83 35 of of IN cord-326740-1fjr9qr4 83 36 customers customer NNS cord-326740-1fjr9qr4 83 37 in in IN cord-326740-1fjr9qr4 83 38 a a DT cord-326740-1fjr9qr4 83 39 store store NN cord-326740-1fjr9qr4 83 40 increases increase NNS cord-326740-1fjr9qr4 83 41 , , , cord-326740-1fjr9qr4 83 42 we -PRON- PRP cord-326740-1fjr9qr4 83 43 estimate estimate VBP cord-326740-1fjr9qr4 83 44 the the DT cord-326740-1fjr9qr4 83 45 risk risk NN cord-326740-1fjr9qr4 83 46 of of IN cord-326740-1fjr9qr4 83 47 infection infection NN cord-326740-1fjr9qr4 83 48 as as IN cord-326740-1fjr9qr4 83 49 proportional proportional JJ cord-326740-1fjr9qr4 83 50 to to IN cord-326740-1fjr9qr4 83 51 . . . cord-326740-1fjr9qr4 84 1 That that RB cord-326740-1fjr9qr4 84 2 is is RB cord-326740-1fjr9qr4 84 3 , , , cord-326740-1fjr9qr4 84 4 when when WRB cord-326740-1fjr9qr4 84 5 L L NNP cord-326740-1fjr9qr4 84 6 customers customer NNS cord-326740-1fjr9qr4 84 7 are be VBP cord-326740-1fjr9qr4 84 8 present present JJ cord-326740-1fjr9qr4 84 9 in in IN cord-326740-1fjr9qr4 84 10 the the DT cord-326740-1fjr9qr4 84 11 store store NN cord-326740-1fjr9qr4 84 12 , , , cord-326740-1fjr9qr4 84 13 each each DT cord-326740-1fjr9qr4 84 14 one one NN cord-326740-1fjr9qr4 84 15 can can MD cord-326740-1fjr9qr4 84 16 be be VB cord-326740-1fjr9qr4 84 17 infected infect VBN cord-326740-1fjr9qr4 84 18 by by IN cord-326740-1fjr9qr4 84 19 the the DT cord-326740-1fjr9qr4 84 20 other other JJ cord-326740-1fjr9qr4 84 21 customers customer NNS cord-326740-1fjr9qr4 84 22 . . . cord-326740-1fjr9qr4 85 1 Also also RB cord-326740-1fjr9qr4 85 2 , , , cord-326740-1fjr9qr4 85 3 the the DT cord-326740-1fjr9qr4 85 4 risk risk NN cord-326740-1fjr9qr4 85 5 of of IN cord-326740-1fjr9qr4 85 6 infection infection NN cord-326740-1fjr9qr4 85 7 is be VBZ cord-326740-1fjr9qr4 85 8 lower low JJR cord-326740-1fjr9qr4 85 9 in in IN cord-326740-1fjr9qr4 85 10 more more RBR cord-326740-1fjr9qr4 85 11 - - HYPH cord-326740-1fjr9qr4 85 12 open open JJ cord-326740-1fjr9qr4 85 13 areas area NNS cord-326740-1fjr9qr4 85 14 and and CC cord-326740-1fjr9qr4 85 15 could could MD cord-326740-1fjr9qr4 85 16 depend depend VB cord-326740-1fjr9qr4 85 17 on on IN cord-326740-1fjr9qr4 85 18 whether whether IN cord-326740-1fjr9qr4 85 19 social social JJ cord-326740-1fjr9qr4 85 20 distance distance NN cord-326740-1fjr9qr4 85 21 can can MD cord-326740-1fjr9qr4 85 22 be be VB cord-326740-1fjr9qr4 85 23 and and CC cord-326740-1fjr9qr4 85 24 is be VBZ cord-326740-1fjr9qr4 85 25 maintained maintain VBN cord-326740-1fjr9qr4 85 26 . . . cord-326740-1fjr9qr4 86 1 Therefore therefore RB cord-326740-1fjr9qr4 86 2 , , , cord-326740-1fjr9qr4 86 3 in in IN cord-326740-1fjr9qr4 86 4 this this DT cord-326740-1fjr9qr4 86 5 section section NN cord-326740-1fjr9qr4 86 6 we -PRON- PRP cord-326740-1fjr9qr4 86 7 calculate calculate VBP cord-326740-1fjr9qr4 86 8 the the DT cord-326740-1fjr9qr4 86 9 combined combined JJ cord-326740-1fjr9qr4 86 10 risk risk NN cord-326740-1fjr9qr4 86 11 of of IN cord-326740-1fjr9qr4 86 12 infection infection NN cord-326740-1fjr9qr4 86 13 for for IN cord-326740-1fjr9qr4 86 14 customers customer NNS cord-326740-1fjr9qr4 86 15 along along IN cord-326740-1fjr9qr4 86 16 their -PRON- PRP$ cord-326740-1fjr9qr4 86 17 waiting waiting NN cord-326740-1fjr9qr4 86 18 , , , cord-326740-1fjr9qr4 86 19 shopping shopping NN cord-326740-1fjr9qr4 86 20 , , , cord-326740-1fjr9qr4 86 21 and and CC cord-326740-1fjr9qr4 86 22 payment payment NN cord-326740-1fjr9qr4 86 23 routes route NNS cord-326740-1fjr9qr4 86 24 ( ( -LRB- cord-326740-1fjr9qr4 86 25 phases phase NNS cord-326740-1fjr9qr4 86 26 ) ) -RRB- cord-326740-1fjr9qr4 86 27 . . . cord-326740-1fjr9qr4 87 1 Let let VB cord-326740-1fjr9qr4 87 2 L L NNP cord-326740-1fjr9qr4 87 3 1 1 CD cord-326740-1fjr9qr4 87 4 SHOP shop NN cord-326740-1fjr9qr4 87 5 denote denote VBP cord-326740-1fjr9qr4 87 6 the the DT cord-326740-1fjr9qr4 87 7 number number NN cord-326740-1fjr9qr4 87 8 of of IN cord-326740-1fjr9qr4 87 9 shoppers shopper NNS cord-326740-1fjr9qr4 87 10 and and CC cord-326740-1fjr9qr4 87 11 let let VB cord-326740-1fjr9qr4 87 12 L l NN cord-326740-1fjr9qr4 87 13 1 1 CD cord-326740-1fjr9qr4 87 14 OUT out NN cord-326740-1fjr9qr4 87 15 denote denote VB cord-326740-1fjr9qr4 87 16 the the DT cord-326740-1fjr9qr4 87 17 number number NN cord-326740-1fjr9qr4 87 18 of of IN cord-326740-1fjr9qr4 87 19 customers customer NNS cord-326740-1fjr9qr4 87 20 lining line VBG cord-326740-1fjr9qr4 87 21 up up RP cord-326740-1fjr9qr4 87 22 outside outside IN cord-326740-1fjr9qr4 87 23 the the DT cord-326740-1fjr9qr4 87 24 store store NN cord-326740-1fjr9qr4 87 25 with with IN cord-326740-1fjr9qr4 87 26 L l NN cord-326740-1fjr9qr4 87 27 1 1 CD cord-326740-1fjr9qr4 87 28 = = NFP cord-326740-1fjr9qr4 88 1 L L NNP cord-326740-1fjr9qr4 88 2 1 1 CD cord-326740-1fjr9qr4 88 3 SHOP shop NN cord-326740-1fjr9qr4 88 4 + + CC cord-326740-1fjr9qr4 89 1 L l NN cord-326740-1fjr9qr4 89 2 1 1 CD cord-326740-1fjr9qr4 89 3 OUT out NN cord-326740-1fjr9qr4 89 4 . . . cord-326740-1fjr9qr4 90 1 We -PRON- PRP cord-326740-1fjr9qr4 90 2 start start VBP cord-326740-1fjr9qr4 90 3 by by IN cord-326740-1fjr9qr4 90 4 calculating calculate VBG cord-326740-1fjr9qr4 90 5 . . . cord-326740-1fjr9qr4 91 1 The the DT cord-326740-1fjr9qr4 91 2 risk risk NN cord-326740-1fjr9qr4 91 3 to to IN cord-326740-1fjr9qr4 91 4 shoppers shopper NNS cord-326740-1fjr9qr4 91 5 of of IN cord-326740-1fjr9qr4 91 6 being be VBG cord-326740-1fjr9qr4 91 7 infected infect VBN cord-326740-1fjr9qr4 91 8 is be VBZ cord-326740-1fjr9qr4 91 9 considered consider VBN cord-326740-1fjr9qr4 91 10 proportional proportional JJ cord-326740-1fjr9qr4 91 11 to to IN cord-326740-1fjr9qr4 91 12 . . . cord-326740-1fjr9qr4 92 1 The the DT cord-326740-1fjr9qr4 92 2 risk risk NN cord-326740-1fjr9qr4 92 3 of of IN cord-326740-1fjr9qr4 92 4 customers customer NNS cord-326740-1fjr9qr4 92 5 waiting wait VBG cord-326740-1fjr9qr4 92 6 outside outside IN cord-326740-1fjr9qr4 92 7 the the DT cord-326740-1fjr9qr4 92 8 store store NN cord-326740-1fjr9qr4 92 9 is be VBZ cord-326740-1fjr9qr4 92 10 proportional proportional JJ cord-326740-1fjr9qr4 92 11 to to IN cord-326740-1fjr9qr4 92 12 . . . cord-326740-1fjr9qr4 93 1 , , , cord-326740-1fjr9qr4 93 2 , , , cord-326740-1fjr9qr4 93 3 , , , cord-326740-1fjr9qr4 93 4 ... ... NFP cord-326740-1fjr9qr4 93 5 , , , cord-326740-1fjr9qr4 93 6 , , , cord-326740-1fjr9qr4 93 7 1 1 CD cord-326740-1fjr9qr4 93 8 , , , cord-326740-1fjr9qr4 93 9 2 2 CD cord-326740-1fjr9qr4 93 10 , , , cord-326740-1fjr9qr4 93 11 ... ... : cord-326740-1fjr9qr4 94 1 , , , cord-326740-1fjr9qr4 94 2 1,0 1,0 CD cord-326740-1fjr9qr4 94 3 , , , cord-326740-1fjr9qr4 95 1 0,1 0,1 LS cord-326740-1fjr9qr4 95 2 , , , cord-326740-1fjr9qr4 95 3 ... ... : cord-326740-1fjr9qr4 96 1 , , , cord-326740-1fjr9qr4 96 2 ; ; : cord-326740-1fjr9qr4 96 3 2 2 CD cord-326740-1fjr9qr4 96 4 2 2 CD cord-326740-1fjr9qr4 96 5 2 2 CD cord-326740-1fjr9qr4 96 6 2 2 CD cord-326740-1fjr9qr4 96 7 2 2 CD cord-326740-1fjr9qr4 96 8 2 2 CD cord-326740-1fjr9qr4 96 9 2 2 CD cord-326740-1fjr9qr4 96 10 2 2 CD cord-326740-1fjr9qr4 96 11 1 1 CD cord-326740-1fjr9qr4 96 12 , , , cord-326740-1fjr9qr4 96 13 , , , cord-326740-1fjr9qr4 96 14 , , , cord-326740-1fjr9qr4 96 15 ... ... NFP cord-326740-1fjr9qr4 96 16 , , , cord-326740-1fjr9qr4 96 17 , , , cord-326740-1fjr9qr4 96 18 ( ( -LRB- cord-326740-1fjr9qr4 96 19 1 1 CD cord-326740-1fjr9qr4 96 20 ) ) -RRB- cord-326740-1fjr9qr4 96 21 , , , cord-326740-1fjr9qr4 96 22 ( ( -LRB- cord-326740-1fjr9qr4 96 23 2 2 LS cord-326740-1fjr9qr4 96 24 ) ) -RRB- cord-326740-1fjr9qr4 96 25 , , , cord-326740-1fjr9qr4 96 26 ... ... NFP cord-326740-1fjr9qr4 96 27 , , , cord-326740-1fjr9qr4 96 28 1,0 1,0 CD cord-326740-1fjr9qr4 96 29 , , , cord-326740-1fjr9qr4 96 30 0,1 0,1 CD cord-326740-1fjr9qr4 96 31 , , , cord-326740-1fjr9qr4 96 32 ... ... NFP cord-326740-1fjr9qr4 96 33 , , , cord-326740-1fjr9qr4 96 34 ; ; : cord-326740-1fjr9qr4 96 35 be be VB cord-326740-1fjr9qr4 96 36 four four CD cord-326740-1fjr9qr4 96 37 sets set NNS cord-326740-1fjr9qr4 96 38 of of IN cord-326740-1fjr9qr4 96 39 column column NN cord-326740-1fjr9qr4 96 40 vectors vector NNS cord-326740-1fjr9qr4 96 41 , , , cord-326740-1fjr9qr4 96 42 each each DT cord-326740-1fjr9qr4 96 43 of of IN cord-326740-1fjr9qr4 96 44 size size NN cord-326740-1fjr9qr4 96 45 . . . cord-326740-1fjr9qr4 97 1 Then then RB cord-326740-1fjr9qr4 97 2 , , , cord-326740-1fjr9qr4 97 3 _SP cord-326740-1fjr9qr4 97 4 When when WRB cord-326740-1fjr9qr4 97 5 the the DT cord-326740-1fjr9qr4 97 6 system system NN cord-326740-1fjr9qr4 97 7 is be VBZ cord-326740-1fjr9qr4 97 8 stable stable JJ cord-326740-1fjr9qr4 97 9 , , , cord-326740-1fjr9qr4 97 10 the the DT cord-326740-1fjr9qr4 97 11 mean mean JJ cord-326740-1fjr9qr4 97 12 rate rate NN cord-326740-1fjr9qr4 97 13 of of IN cord-326740-1fjr9qr4 97 14 arrival arrival NN cord-326740-1fjr9qr4 97 15 rate rate NN cord-326740-1fjr9qr4 97 16 at at IN cord-326740-1fjr9qr4 97 17 the the DT cord-326740-1fjr9qr4 97 18 shopping shopping NN cord-326740-1fjr9qr4 97 19 phase phase NN cord-326740-1fjr9qr4 97 20 is be VBZ cord-326740-1fjr9qr4 97 21 . . . cord-326740-1fjr9qr4 98 1 λ λ NNP cord-326740-1fjr9qr4 98 2 Similarly similarly RB cord-326740-1fjr9qr4 98 3 , , , cord-326740-1fjr9qr4 98 4 the the DT cord-326740-1fjr9qr4 98 5 mean mean JJ cord-326740-1fjr9qr4 98 6 rate rate NN cord-326740-1fjr9qr4 98 7 of of IN cord-326740-1fjr9qr4 98 8 arrival arrival NN cord-326740-1fjr9qr4 98 9 at at IN cord-326740-1fjr9qr4 98 10 the the DT cord-326740-1fjr9qr4 98 11 payment payment NN cord-326740-1fjr9qr4 98 12 phase phase NN cord-326740-1fjr9qr4 98 13 is be VBZ cord-326740-1fjr9qr4 98 14 also also RB cord-326740-1fjr9qr4 98 15 . . . cord-326740-1fjr9qr4 99 1 Applying apply VBG cord-326740-1fjr9qr4 99 2 Little Little NNP cord-326740-1fjr9qr4 99 3 's 's POS cord-326740-1fjr9qr4 99 4 Law law NN cord-326740-1fjr9qr4 99 5 , , , cord-326740-1fjr9qr4 99 6 one one PRP cord-326740-1fjr9qr4 99 7 can can MD cord-326740-1fjr9qr4 99 8 λ λ NN cord-326740-1fjr9qr4 99 9 calculate calculate VB cord-326740-1fjr9qr4 99 10 the the DT cord-326740-1fjr9qr4 99 11 mean mean NN cord-326740-1fjr9qr4 99 12 waiting waiting NN cord-326740-1fjr9qr4 99 13 times time NNS cord-326740-1fjr9qr4 99 14 : : : cord-326740-1fjr9qr4 99 15 3 3 CD cord-326740-1fjr9qr4 99 16 . . . cord-326740-1fjr9qr4 100 1 The the DT cord-326740-1fjr9qr4 100 2 NM NM NNP cord-326740-1fjr9qr4 100 3 - - HYPH cord-326740-1fjr9qr4 100 4 model model NN cord-326740-1fjr9qr4 100 5 : : : cord-326740-1fjr9qr4 101 1 Maximum maximum JJ cord-326740-1fjr9qr4 101 2 number number NN cord-326740-1fjr9qr4 101 3 of of IN cord-326740-1fjr9qr4 101 4 customers customer NNS cord-326740-1fjr9qr4 101 5 at at IN cord-326740-1fjr9qr4 101 6 the the DT cord-326740-1fjr9qr4 101 7 cashier cashier NN cord-326740-1fjr9qr4 101 8 area area NN cord-326740-1fjr9qr4 101 9 and and CC cord-326740-1fjr9qr4 101 10 shopping shopping NN cord-326740-1fjr9qr4 101 11 inside inside IN cord-326740-1fjr9qr4 101 12 the the DT cord-326740-1fjr9qr4 101 13 store store NN cord-326740-1fjr9qr4 101 14 We -PRON- PRP cord-326740-1fjr9qr4 101 15 now now RB cord-326740-1fjr9qr4 101 16 model model VBP cord-326740-1fjr9qr4 101 17 a a DT cord-326740-1fjr9qr4 101 18 setting setting NN cord-326740-1fjr9qr4 101 19 in in IN cord-326740-1fjr9qr4 101 20 which which WDT cord-326740-1fjr9qr4 101 21 the the DT cord-326740-1fjr9qr4 101 22 store store NN cord-326740-1fjr9qr4 101 23 sets set VBZ cord-326740-1fjr9qr4 101 24 aside aside RB cord-326740-1fjr9qr4 101 25 a a DT cord-326740-1fjr9qr4 101 26 separate separate JJ cord-326740-1fjr9qr4 101 27 waiting waiting NN cord-326740-1fjr9qr4 101 28 space space NN cord-326740-1fjr9qr4 101 29 near near IN cord-326740-1fjr9qr4 101 30 the the DT cord-326740-1fjr9qr4 101 31 cashiers cashier NNS cord-326740-1fjr9qr4 101 32 for for IN cord-326740-1fjr9qr4 101 33 at at RB cord-326740-1fjr9qr4 101 34 most most JJS cord-326740-1fjr9qr4 101 35 N n CD cord-326740-1fjr9qr4 101 36 ≥ ≥ CD cord-326740-1fjr9qr4 101 37 0 0 CD cord-326740-1fjr9qr4 101 38 customers customer NNS cord-326740-1fjr9qr4 101 39 in in IN cord-326740-1fjr9qr4 101 40 the the DT cord-326740-1fjr9qr4 101 41 payment payment NN cord-326740-1fjr9qr4 101 42 phase phase NN cord-326740-1fjr9qr4 101 43 and and CC cord-326740-1fjr9qr4 101 44 those those DT cord-326740-1fjr9qr4 101 45 customers customer NNS cord-326740-1fjr9qr4 101 46 wait wait VBP cord-326740-1fjr9qr4 101 47 in in IN cord-326740-1fjr9qr4 101 48 a a DT cord-326740-1fjr9qr4 101 49 single single JJ cord-326740-1fjr9qr4 101 50 line line NN cord-326740-1fjr9qr4 101 51 in in IN cord-326740-1fjr9qr4 101 52 the the DT cord-326740-1fjr9qr4 101 53 designated designated JJ cord-326740-1fjr9qr4 101 54 area area NN cord-326740-1fjr9qr4 101 55 ( ( -LRB- cord-326740-1fjr9qr4 101 56 if if IN cord-326740-1fjr9qr4 101 57 necessary necessary JJ cord-326740-1fjr9qr4 101 58 ) ) -RRB- cord-326740-1fjr9qr4 101 59 to to TO cord-326740-1fjr9qr4 101 60 be be VB cord-326740-1fjr9qr4 101 61 admitted admit VBN cord-326740-1fjr9qr4 101 62 by by IN cord-326740-1fjr9qr4 101 63 the the DT cord-326740-1fjr9qr4 101 64 next next JJ cord-326740-1fjr9qr4 101 65 free free JJ cord-326740-1fjr9qr4 101 66 cashier cashier NN cord-326740-1fjr9qr4 101 67 . . . cord-326740-1fjr9qr4 102 1 As as IN cord-326740-1fjr9qr4 102 2 in in IN cord-326740-1fjr9qr4 102 3 the the DT cord-326740-1fjr9qr4 102 4 M M NNP cord-326740-1fjr9qr4 102 5 - - HYPH cord-326740-1fjr9qr4 102 6 model model NN cord-326740-1fjr9qr4 102 7 , , , cord-326740-1fjr9qr4 102 8 the the DT cord-326740-1fjr9qr4 102 9 authorities authority NNS cord-326740-1fjr9qr4 102 10 in in IN cord-326740-1fjr9qr4 102 11 this this DT cord-326740-1fjr9qr4 102 12 model model NN cord-326740-1fjr9qr4 102 13 have have VBP cord-326740-1fjr9qr4 102 14 imposed impose VBN cord-326740-1fjr9qr4 102 15 a a DT cord-326740-1fjr9qr4 102 16 limit limit NN cord-326740-1fjr9qr4 102 17 , , , cord-326740-1fjr9qr4 102 18 M M NNP cord-326740-1fjr9qr4 102 19 , , , cord-326740-1fjr9qr4 102 20 on on IN cord-326740-1fjr9qr4 102 21 the the DT cord-326740-1fjr9qr4 102 22 total total JJ cord-326740-1fjr9qr4 102 23 number number NN cord-326740-1fjr9qr4 102 24 of of IN cord-326740-1fjr9qr4 102 25 customers customer NNS cord-326740-1fjr9qr4 102 26 allowed allow VBN cord-326740-1fjr9qr4 102 27 inside inside IN cord-326740-1fjr9qr4 102 28 the the DT cord-326740-1fjr9qr4 102 29 store store NN cord-326740-1fjr9qr4 102 30 . . . cord-326740-1fjr9qr4 103 1 Thus thus RB cord-326740-1fjr9qr4 103 2 , , , cord-326740-1fjr9qr4 103 3 in in IN cord-326740-1fjr9qr4 103 4 this this DT cord-326740-1fjr9qr4 103 5 setting setting NN cord-326740-1fjr9qr4 103 6 , , , cord-326740-1fjr9qr4 103 7 the the DT cord-326740-1fjr9qr4 103 8 store store NN cord-326740-1fjr9qr4 103 9 is be VBZ cord-326740-1fjr9qr4 103 10 divided divide VBN cord-326740-1fjr9qr4 103 11 into into IN cord-326740-1fjr9qr4 103 12 two two CD cord-326740-1fjr9qr4 103 13 separate separate JJ cord-326740-1fjr9qr4 103 14 areas area NNS cord-326740-1fjr9qr4 103 15 : : : cord-326740-1fjr9qr4 103 16 ( ( -LRB- cord-326740-1fjr9qr4 103 17 i i NN cord-326740-1fjr9qr4 103 18 ) ) -RRB- cord-326740-1fjr9qr4 104 1 the the DT cord-326740-1fjr9qr4 104 2 payment payment NN cord-326740-1fjr9qr4 104 3 area area NN cord-326740-1fjr9qr4 104 4 with with IN cord-326740-1fjr9qr4 104 5 c c NN cord-326740-1fjr9qr4 104 6 ≥ ≥ CD cord-326740-1fjr9qr4 104 7 1 1 CD cord-326740-1fjr9qr4 104 8 parallel parallel JJ cord-326740-1fjr9qr4 104 9 cashiers cashier NNS cord-326740-1fjr9qr4 104 10 and and CC cord-326740-1fjr9qr4 104 11 waiting wait VBG cord-326740-1fjr9qr4 104 12 space space NN cord-326740-1fjr9qr4 104 13 of of IN cord-326740-1fjr9qr4 104 14 size size NN cord-326740-1fjr9qr4 104 15 N n CD cord-326740-1fjr9qr4 104 16 customers customer NNS cord-326740-1fjr9qr4 104 17 and and CC cord-326740-1fjr9qr4 104 18 ( ( -LRB- cord-326740-1fjr9qr4 104 19 ii ii NN cord-326740-1fjr9qr4 104 20 ) ) -RRB- cord-326740-1fjr9qr4 104 21 the the DT cord-326740-1fjr9qr4 104 22 shopping shopping NN cord-326740-1fjr9qr4 104 23 area area NN cord-326740-1fjr9qr4 104 24 , , , cord-326740-1fjr9qr4 104 25 in in IN cord-326740-1fjr9qr4 104 26 which which WDT cord-326740-1fjr9qr4 104 27 the the DT cord-326740-1fjr9qr4 104 28 maximum maximum JJ cord-326740-1fjr9qr4 104 29 number number NN cord-326740-1fjr9qr4 104 30 of of IN cord-326740-1fjr9qr4 104 31 customers customer NNS cord-326740-1fjr9qr4 104 32 allowed allow VBN cord-326740-1fjr9qr4 104 33 , , , cord-326740-1fjr9qr4 104 34 K. K. NNP cord-326740-1fjr9qr4 105 1 Thus thus RB cord-326740-1fjr9qr4 105 2 , , , cord-326740-1fjr9qr4 105 3 the the DT cord-326740-1fjr9qr4 105 4 maximum maximum JJ cord-326740-1fjr9qr4 105 5 number number NN cord-326740-1fjr9qr4 105 6 of of IN cord-326740-1fjr9qr4 105 7 customers customer NNS cord-326740-1fjr9qr4 105 8 is be VBZ cord-326740-1fjr9qr4 105 9 the the DT cord-326740-1fjr9qr4 105 10 store store NN cord-326740-1fjr9qr4 105 11 is be VBZ cord-326740-1fjr9qr4 105 12 . . . cord-326740-1fjr9qr4 106 1 = = NFP cord-326740-1fjr9qr4 107 1 + + CC cord-326740-1fjr9qr4 107 2 + + CC cord-326740-1fjr9qr4 108 1 In in IN cord-326740-1fjr9qr4 108 2 this this DT cord-326740-1fjr9qr4 108 3 model model NN cord-326740-1fjr9qr4 108 4 , , , cord-326740-1fjr9qr4 108 5 a a DT cord-326740-1fjr9qr4 108 6 customer customer NN cord-326740-1fjr9qr4 108 7 first first RB cord-326740-1fjr9qr4 108 8 spends spend VBZ cord-326740-1fjr9qr4 108 9 a a DT cord-326740-1fjr9qr4 108 10 random random JJ cord-326740-1fjr9qr4 108 11 period period NN cord-326740-1fjr9qr4 108 12 of of IN cord-326740-1fjr9qr4 108 13 time time NN cord-326740-1fjr9qr4 108 14 in in IN cord-326740-1fjr9qr4 108 15 the the DT cord-326740-1fjr9qr4 108 16 shopping shopping NN cord-326740-1fjr9qr4 108 17 phase phase NN cord-326740-1fjr9qr4 108 18 / / SYM cord-326740-1fjr9qr4 108 19 area area NN cord-326740-1fjr9qr4 108 20 that that WDT cord-326740-1fjr9qr4 108 21 is be VBZ cord-326740-1fjr9qr4 108 22 exponentially exponentially RB cord-326740-1fjr9qr4 108 23 distributed distribute VBN cord-326740-1fjr9qr4 108 24 with with IN cord-326740-1fjr9qr4 108 25 mean mean JJ cord-326740-1fjr9qr4 108 26 1 1 CD cord-326740-1fjr9qr4 108 27 / / SYM cord-326740-1fjr9qr4 108 28 ξ ξ NNS cord-326740-1fjr9qr4 108 29 and and CC cord-326740-1fjr9qr4 108 30 then then RB cord-326740-1fjr9qr4 108 31 proceeds proceed VBZ cord-326740-1fjr9qr4 108 32 to to IN cord-326740-1fjr9qr4 108 33 the the DT cord-326740-1fjr9qr4 108 34 payment payment NN cord-326740-1fjr9qr4 108 35 phase phase NN cord-326740-1fjr9qr4 108 36 / / SYM cord-326740-1fjr9qr4 108 37 area area NN cord-326740-1fjr9qr4 108 38 . . . cord-326740-1fjr9qr4 109 1 When when WRB cord-326740-1fjr9qr4 109 2 there there EX cord-326740-1fjr9qr4 109 3 are be VBP cord-326740-1fjr9qr4 109 4 exactly exactly RB cord-326740-1fjr9qr4 109 5 c c NN cord-326740-1fjr9qr4 109 6 + + CC cord-326740-1fjr9qr4 109 7 N n CD cord-326740-1fjr9qr4 109 8 payers payer NNS cord-326740-1fjr9qr4 109 9 , , , cord-326740-1fjr9qr4 109 10 this this DT cord-326740-1fjr9qr4 109 11 customer customer NN cord-326740-1fjr9qr4 109 12 " " `` cord-326740-1fjr9qr4 109 13 orbits orbit NNS cord-326740-1fjr9qr4 109 14 " " '' cord-326740-1fjr9qr4 109 15 in in IN cord-326740-1fjr9qr4 109 16 the the DT cord-326740-1fjr9qr4 109 17 shopping shopping NN cord-326740-1fjr9qr4 109 18 area area NN cord-326740-1fjr9qr4 109 19 for for IN cord-326740-1fjr9qr4 109 20 another another DT cord-326740-1fjr9qr4 109 21 exponentially exponentially RB cord-326740-1fjr9qr4 109 22 distributed distribute VBN cord-326740-1fjr9qr4 109 23 period period NN cord-326740-1fjr9qr4 109 24 of of IN cord-326740-1fjr9qr4 109 25 time time NN cord-326740-1fjr9qr4 109 26 with with IN cord-326740-1fjr9qr4 109 27 the the DT cord-326740-1fjr9qr4 109 28 same same JJ cord-326740-1fjr9qr4 109 29 mean mean NN cord-326740-1fjr9qr4 109 30 1 1 CD cord-326740-1fjr9qr4 109 31 / / SYM cord-326740-1fjr9qr4 109 32 ξ ξ NNS cord-326740-1fjr9qr4 109 33 ( ( -LRB- cord-326740-1fjr9qr4 109 34 see see UH cord-326740-1fjr9qr4 109 35 , , , cord-326740-1fjr9qr4 109 36 e.g. e.g. RB cord-326740-1fjr9qr4 109 37 , , , cord-326740-1fjr9qr4 109 38 Avrachenkov Avrachenkov NNP cord-326740-1fjr9qr4 109 39 et et NNP cord-326740-1fjr9qr4 109 40 al al NNP cord-326740-1fjr9qr4 109 41 . . NNP cord-326740-1fjr9qr4 109 42 , , , cord-326740-1fjr9qr4 109 43 2014 2014 CD cord-326740-1fjr9qr4 109 44 ; ; : cord-326740-1fjr9qr4 109 45 Perel Perel NNP cord-326740-1fjr9qr4 109 46 and and CC cord-326740-1fjr9qr4 109 47 Yechiali Yechiali NNP cord-326740-1fjr9qr4 109 48 , , , cord-326740-1fjr9qr4 109 49 2014 2014 CD cord-326740-1fjr9qr4 109 50 ) ) -RRB- cord-326740-1fjr9qr4 109 51 . . . cord-326740-1fjr9qr4 110 1 Otherwise otherwise RB cord-326740-1fjr9qr4 110 2 , , , cord-326740-1fjr9qr4 110 3 when when WRB cord-326740-1fjr9qr4 110 4 the the DT cord-326740-1fjr9qr4 110 5 number number NN cord-326740-1fjr9qr4 110 6 of of IN cord-326740-1fjr9qr4 110 7 customers customer NNS cord-326740-1fjr9qr4 110 8 in in IN cord-326740-1fjr9qr4 110 9 the the DT cord-326740-1fjr9qr4 110 10 cashier cashier NN cord-326740-1fjr9qr4 110 11 area area NN cord-326740-1fjr9qr4 110 12 is be VBZ cord-326740-1fjr9qr4 110 13 less less JJR cord-326740-1fjr9qr4 110 14 than than IN cord-326740-1fjr9qr4 110 15 c c NN cord-326740-1fjr9qr4 111 1 + + CC cord-326740-1fjr9qr4 111 2 N n CD cord-326740-1fjr9qr4 111 3 , , , cord-326740-1fjr9qr4 111 4 the the DT cord-326740-1fjr9qr4 111 5 customer customer NN cord-326740-1fjr9qr4 111 6 enters enter VBZ cord-326740-1fjr9qr4 111 7 the the DT cord-326740-1fjr9qr4 111 8 cashier cashier NN cord-326740-1fjr9qr4 111 9 area area NN cord-326740-1fjr9qr4 111 10 and and CC cord-326740-1fjr9qr4 111 11 becomes become VBZ cord-326740-1fjr9qr4 111 12 a a DT cord-326740-1fjr9qr4 111 13 payer payer NN cord-326740-1fjr9qr4 111 14 . . . cord-326740-1fjr9qr4 112 1 When when WRB cord-326740-1fjr9qr4 112 2 at at RB cord-326740-1fjr9qr4 112 3 least least RBS cord-326740-1fjr9qr4 112 4 one one CD cord-326740-1fjr9qr4 112 5 of of IN cord-326740-1fjr9qr4 112 6 the the DT cord-326740-1fjr9qr4 112 7 cashiers cashier NNS cord-326740-1fjr9qr4 112 8 is be VBZ cord-326740-1fjr9qr4 112 9 not not RB cord-326740-1fjr9qr4 112 10 busy busy JJ cord-326740-1fjr9qr4 112 11 , , , cord-326740-1fjr9qr4 112 12 the the DT cord-326740-1fjr9qr4 112 13 payer payer NN cord-326740-1fjr9qr4 112 14 proceeds proceed VBZ cord-326740-1fjr9qr4 112 15 directly directly RB cord-326740-1fjr9qr4 112 16 to to IN cord-326740-1fjr9qr4 112 17 a a DT cord-326740-1fjr9qr4 112 18 cashier cashier NN cord-326740-1fjr9qr4 112 19 and and CC cord-326740-1fjr9qr4 112 20 pays pay VBZ cord-326740-1fjr9qr4 112 21 . . . cord-326740-1fjr9qr4 113 1 As as IN cord-326740-1fjr9qr4 113 2 in in IN cord-326740-1fjr9qr4 113 3 the the DT cord-326740-1fjr9qr4 113 4 M M NNP cord-326740-1fjr9qr4 113 5 - - HYPH cord-326740-1fjr9qr4 113 6 model model NN cord-326740-1fjr9qr4 113 7 , , , cord-326740-1fjr9qr4 113 8 the the DT cord-326740-1fjr9qr4 113 9 payment payment NN cord-326740-1fjr9qr4 113 10 ( ( -LRB- cord-326740-1fjr9qr4 113 11 service service NN cord-326740-1fjr9qr4 113 12 ) ) -RRB- cord-326740-1fjr9qr4 113 13 duration duration NN cord-326740-1fjr9qr4 113 14 is be VBZ cord-326740-1fjr9qr4 113 15 exponentially exponentially RB cord-326740-1fjr9qr4 113 16 distributed distribute VBN cord-326740-1fjr9qr4 113 17 with with IN cord-326740-1fjr9qr4 113 18 mean mean JJ cord-326740-1fjr9qr4 113 19 1/µ. 1/µ. CD cord-326740-1fjr9qr4 114 1 All all DT cord-326740-1fjr9qr4 114 2 shopping shopping NN cord-326740-1fjr9qr4 114 3 , , , cord-326740-1fjr9qr4 114 4 service service NN cord-326740-1fjr9qr4 114 5 , , , cord-326740-1fjr9qr4 114 6 and and CC cord-326740-1fjr9qr4 114 7 orbit orbit NN cord-326740-1fjr9qr4 114 8 times time NNS cord-326740-1fjr9qr4 114 9 are be VBP cord-326740-1fjr9qr4 114 10 independent independent JJ cord-326740-1fjr9qr4 114 11 of of IN cord-326740-1fjr9qr4 114 12 each each DT cord-326740-1fjr9qr4 114 13 other other JJ cord-326740-1fjr9qr4 114 14 and and CC cord-326740-1fjr9qr4 114 15 independent independent JJ cord-326740-1fjr9qr4 114 16 of of IN cord-326740-1fjr9qr4 114 17 the the DT cord-326740-1fjr9qr4 114 18 arrival arrival NN cord-326740-1fjr9qr4 114 19 process process NN cord-326740-1fjr9qr4 114 20 . . . cord-326740-1fjr9qr4 115 1 Let let VB cord-326740-1fjr9qr4 115 2 L L NNP cord-326740-1fjr9qr4 115 3 1 1 CD cord-326740-1fjr9qr4 115 4 SHOP shop NN cord-326740-1fjr9qr4 115 5 denote denote VBP cord-326740-1fjr9qr4 115 6 the the DT cord-326740-1fjr9qr4 115 7 number number NN cord-326740-1fjr9qr4 115 8 of of IN cord-326740-1fjr9qr4 115 9 customers customer NNS cord-326740-1fjr9qr4 115 10 in in IN cord-326740-1fjr9qr4 115 11 the the DT cord-326740-1fjr9qr4 115 12 shopping shopping NN cord-326740-1fjr9qr4 115 13 area area NN cord-326740-1fjr9qr4 115 14 and and CC cord-326740-1fjr9qr4 115 15 let let VB cord-326740-1fjr9qr4 115 16 L l NN cord-326740-1fjr9qr4 115 17 1 1 CD cord-326740-1fjr9qr4 115 18 OUT out NN cord-326740-1fjr9qr4 115 19 denote denote VB cord-326740-1fjr9qr4 115 20 the the DT cord-326740-1fjr9qr4 115 21 number number NN cord-326740-1fjr9qr4 115 22 of of IN cord-326740-1fjr9qr4 115 23 customers customer NNS cord-326740-1fjr9qr4 115 24 lining line VBG cord-326740-1fjr9qr4 115 25 up up RP cord-326740-1fjr9qr4 115 26 outside outside IN cord-326740-1fjr9qr4 115 27 the the DT cord-326740-1fjr9qr4 115 28 store store NN cord-326740-1fjr9qr4 115 29 . . . cord-326740-1fjr9qr4 116 1 Let let VB cord-326740-1fjr9qr4 116 2 L l NN cord-326740-1fjr9qr4 116 3 1 1 CD cord-326740-1fjr9qr4 116 4 = = NFP cord-326740-1fjr9qr4 117 1 L L NNP cord-326740-1fjr9qr4 117 2 1 1 CD cord-326740-1fjr9qr4 117 3 SHOP shop NN cord-326740-1fjr9qr4 117 4 + + CC cord-326740-1fjr9qr4 118 1 L l NN cord-326740-1fjr9qr4 118 2 1 1 CD cord-326740-1fjr9qr4 118 3 OUT out NN cord-326740-1fjr9qr4 118 4 . . . cord-326740-1fjr9qr4 119 1 Let let VB cord-326740-1fjr9qr4 119 2 L l NN cord-326740-1fjr9qr4 119 3 2 2 CD cord-326740-1fjr9qr4 119 4 denote denote VB cord-326740-1fjr9qr4 119 5 the the DT cord-326740-1fjr9qr4 119 6 number number NN cord-326740-1fjr9qr4 119 7 of of IN cord-326740-1fjr9qr4 119 8 customers customer NNS cord-326740-1fjr9qr4 119 9 in in IN cord-326740-1fjr9qr4 119 10 the the DT cord-326740-1fjr9qr4 119 11 cashier cashier NN cord-326740-1fjr9qr4 119 12 area area NN cord-326740-1fjr9qr4 119 13 . . . cord-326740-1fjr9qr4 120 1 Then then RB cord-326740-1fjr9qr4 120 2 , , , cord-326740-1fjr9qr4 120 3 the the DT cord-326740-1fjr9qr4 120 4 system system NN cord-326740-1fjr9qr4 120 5 's 's POS cord-326740-1fjr9qr4 120 6 state state NN cord-326740-1fjr9qr4 120 7 - - HYPH cord-326740-1fjr9qr4 120 8 space space NN cord-326740-1fjr9qr4 120 9 is be VBZ cord-326740-1fjr9qr4 120 10 . . . cord-326740-1fjr9qr4 121 1   NNP cord-326740-1fjr9qr4 122 1   NNP cord-326740-1fjr9qr4 122 2 1 1 CD cord-326740-1fjr9qr4 122 3 2 2 CD cord-326740-1fjr9qr4 122 4 ( ( -LRB- cord-326740-1fjr9qr4 122 5 , , , cord-326740-1fjr9qr4 122 6 ) ) -RRB- cord-326740-1fjr9qr4 123 1 ( ( -LRB- cord-326740-1fjr9qr4 123 2 , , , cord-326740-1fjr9qr4 123 3 ) ) -RRB- cord-326740-1fjr9qr4 123 4 : : : cord-326740-1fjr9qr4 123 5 0,1 0,1 CD cord-326740-1fjr9qr4 123 6 , , , cord-326740-1fjr9qr4 123 7 2,3 2,3 CD cord-326740-1fjr9qr4 123 8 , , , cord-326740-1fjr9qr4 123 9 ... ... : cord-326740-1fjr9qr4 123 10 ; ; : cord-326740-1fjr9qr4 123 11 0,1 0,1 CD cord-326740-1fjr9qr4 123 12 , , , cord-326740-1fjr9qr4 123 13 2,3 2,3 CD cord-326740-1fjr9qr4 123 14 , , , cord-326740-1fjr9qr4 123 15 ... ... : cord-326740-1fjr9qr4 124 1 , , , cord-326740-1fjr9qr4 124 2 The the DT cord-326740-1fjr9qr4 124 3 transition transition NN cord-326740-1fjr9qr4 124 4 - - HYPH cord-326740-1fjr9qr4 124 5 rate rate NN cord-326740-1fjr9qr4 124 6 diagram diagram NN cord-326740-1fjr9qr4 124 7 for for IN cord-326740-1fjr9qr4 124 8 this this DT cord-326740-1fjr9qr4 124 9 system system NN cord-326740-1fjr9qr4 124 10 is be VBZ cord-326740-1fjr9qr4 124 11 depicted depict VBN cord-326740-1fjr9qr4 124 12 in in IN cord-326740-1fjr9qr4 124 13 Figure Figure NNP cord-326740-1fjr9qr4 124 14 3 3 CD cord-326740-1fjr9qr4 124 15 . . . cord-326740-1fjr9qr4 124 16 _SP cord-326740-1fjr9qr4 125 1 Matrix Matrix NNP cord-326740-1fjr9qr4 125 2 A A NNP cord-326740-1fjr9qr4 125 3 defines define VBZ cord-326740-1fjr9qr4 125 4 the the DT cord-326740-1fjr9qr4 125 5 underlying underlying JJ cord-326740-1fjr9qr4 125 6 process process NN cord-326740-1fjr9qr4 125 7 of of IN cord-326740-1fjr9qr4 125 8 this this DT cord-326740-1fjr9qr4 125 9 system system NN cord-326740-1fjr9qr4 125 10 and and CC cord-326740-1fjr9qr4 125 11 defines define VBZ cord-326740-1fjr9qr4 125 12 a a DT cord-326740-1fjr9qr4 125 13 truncated truncated JJ cord-326740-1fjr9qr4 125 14 Erlang Erlang NNP cord-326740-1fjr9qr4 125 15 's 's POS cord-326740-1fjr9qr4 125 16 model model NN cord-326740-1fjr9qr4 125 17 of of IN cord-326740-1fjr9qr4 125 18 Poisson Poisson NNP cord-326740-1fjr9qr4 125 19 arrival arrival NN cord-326740-1fjr9qr4 125 20 with with IN cord-326740-1fjr9qr4 125 21 rate rate NN cord-326740-1fjr9qr4 125 22 , , , cord-326740-1fjr9qr4 125 23 c c NN cord-326740-1fjr9qr4 125 24 parallel parallel JJ cord-326740-1fjr9qr4 125 25 exponential exponential JJ cord-326740-1fjr9qr4 125 26 servers server NNS cord-326740-1fjr9qr4 125 27 each each DT cord-326740-1fjr9qr4 125 28 with with IN cord-326740-1fjr9qr4 125 29 rate rate NN cord-326740-1fjr9qr4 125 30 µ µ NN cord-326740-1fjr9qr4 125 31 , , , cord-326740-1fjr9qr4 125 32 and and CC cord-326740-1fjr9qr4 125 33 an an DT cord-326740-1fjr9qr4 125 34 additional additional JJ cord-326740-1fjr9qr4 125 35 K k NN cord-326740-1fjr9qr4 125 36 waiting wait VBG cord-326740-1fjr9qr4 125 37 buffer buffer NN cord-326740-1fjr9qr4 125 38 of of IN cord-326740-1fjr9qr4 125 39 size size NN cord-326740-1fjr9qr4 125 40 N. N. NNP cord-326740-1fjr9qr4 125 41 Figure Figure NNP cord-326740-1fjr9qr4 125 42 4 4 CD cord-326740-1fjr9qr4 125 43 presents present VBZ cord-326740-1fjr9qr4 125 44 its -PRON- PRP$ cord-326740-1fjr9qr4 125 45 transition transition NN cord-326740-1fjr9qr4 125 46 - - HYPH cord-326740-1fjr9qr4 125 47 rate rate NN cord-326740-1fjr9qr4 125 48 diagram diagram NN cord-326740-1fjr9qr4 125 49 . . . cord-326740-1fjr9qr4 125 50 _SP cord-326740-1fjr9qr4 125 51 . . . cord-326740-1fjr9qr4 126 1 Corollary corollary JJ cord-326740-1fjr9qr4 126 2 1 1 CD cord-326740-1fjr9qr4 126 3 specifies specify VBZ cord-326740-1fjr9qr4 126 4 the the DT cord-326740-1fjr9qr4 126 5 value value NN cord-326740-1fjr9qr4 126 6 of of IN cord-326740-1fjr9qr4 126 7 for for IN cord-326740-1fjr9qr4 126 8 some some DT cord-326740-1fjr9qr4 126 9 special special JJ cord-326740-1fjr9qr4 126 10 cases case NNS cord-326740-1fjr9qr4 126 11 . . . cord-326740-1fjr9qr4 126 12 _SP cord-326740-1fjr9qr4 127 1 As as IN cord-326740-1fjr9qr4 127 2 in in IN cord-326740-1fjr9qr4 127 3 the the DT cord-326740-1fjr9qr4 127 4 M M NNP cord-326740-1fjr9qr4 127 5 - - HYPH cord-326740-1fjr9qr4 127 6 model model NN cord-326740-1fjr9qr4 127 7 , , , cord-326740-1fjr9qr4 127 8 the the DT cord-326740-1fjr9qr4 127 9 risk risk NN cord-326740-1fjr9qr4 127 10 of of IN cord-326740-1fjr9qr4 127 11 customers customer NNS cord-326740-1fjr9qr4 127 12 being be VBG cord-326740-1fjr9qr4 127 13 infected infect VBN cord-326740-1fjr9qr4 127 14 at at IN cord-326740-1fjr9qr4 127 15 each each DT cord-326740-1fjr9qr4 127 16 area area NN cord-326740-1fjr9qr4 127 17 is be VBZ cord-326740-1fjr9qr4 127 18 estimated estimate VBN cord-326740-1fjr9qr4 127 19 as as IN cord-326740-1fjr9qr4 127 20 , , , cord-326740-1fjr9qr4 127 21 respectively respectively RB cord-326740-1fjr9qr4 127 22 . . . cord-326740-1fjr9qr4 128 1 The the DT cord-326740-1fjr9qr4 128 2 following follow VBG cord-326740-1fjr9qr4 128 3 proposition proposition NN cord-326740-1fjr9qr4 128 4 shows show VBZ cord-326740-1fjr9qr4 128 5 how how WRB cord-326740-1fjr9qr4 128 6 these these DT cord-326740-1fjr9qr4 128 7 measures measure NNS cord-326740-1fjr9qr4 128 8 are be VBP cord-326740-1fjr9qr4 128 9 calculated calculate VBN cord-326740-1fjr9qr4 128 10 . . . cord-326740-1fjr9qr4 128 11 _SP cord-326740-1fjr9qr4 129 1 ( ( -LRB- cord-326740-1fjr9qr4 129 2 iv iv LS cord-326740-1fjr9qr4 129 3 ) ) -RRB- cord-326740-1fjr9qr4 129 4 Similar similar JJ cord-326740-1fjr9qr4 129 5 to to IN cord-326740-1fjr9qr4 129 6 the the DT cord-326740-1fjr9qr4 129 7 proof proof NN cord-326740-1fjr9qr4 129 8 of of IN cord-326740-1fjr9qr4 129 9 Proposition Proposition NNP cord-326740-1fjr9qr4 129 10 3 3 CD cord-326740-1fjr9qr4 129 11 . . . cord-326740-1fjr9qr4 130 1 ■ ■ NFP cord-326740-1fjr9qr4 130 2 Again again RB cord-326740-1fjr9qr4 130 3 , , , cord-326740-1fjr9qr4 130 4 if if IN cord-326740-1fjr9qr4 130 5 the the DT cord-326740-1fjr9qr4 130 6 system system NN cord-326740-1fjr9qr4 130 7 is be VBZ cord-326740-1fjr9qr4 130 8 stable stable JJ cord-326740-1fjr9qr4 130 9 , , , cord-326740-1fjr9qr4 130 10 the the DT cord-326740-1fjr9qr4 130 11 mean mean JJ cord-326740-1fjr9qr4 130 12 rate rate NN cord-326740-1fjr9qr4 130 13 of of IN cord-326740-1fjr9qr4 130 14 arrival arrival NN cord-326740-1fjr9qr4 130 15 to to IN cord-326740-1fjr9qr4 130 16 the the DT cord-326740-1fjr9qr4 130 17 shopping shopping NN cord-326740-1fjr9qr4 130 18 area area NN cord-326740-1fjr9qr4 130 19 is be VBZ cord-326740-1fjr9qr4 130 20 . . . cord-326740-1fjr9qr4 131 1 Similarly similarly RB cord-326740-1fjr9qr4 131 2 , , , cord-326740-1fjr9qr4 131 3 λ λ NNP cord-326740-1fjr9qr4 131 4 the the DT cord-326740-1fjr9qr4 131 5 mean mean JJ cord-326740-1fjr9qr4 131 6 rate rate NN cord-326740-1fjr9qr4 131 7 of of IN cord-326740-1fjr9qr4 131 8 arrival arrival NN cord-326740-1fjr9qr4 131 9 to to IN cord-326740-1fjr9qr4 131 10 the the DT cord-326740-1fjr9qr4 131 11 cashier cashier NN cord-326740-1fjr9qr4 131 12 area area NN cord-326740-1fjr9qr4 131 13 is be VBZ cord-326740-1fjr9qr4 131 14 also also RB cord-326740-1fjr9qr4 131 15 . . . cord-326740-1fjr9qr4 132 1 Applying apply VBG cord-326740-1fjr9qr4 132 2 Little Little NNP cord-326740-1fjr9qr4 132 3 's 's POS cord-326740-1fjr9qr4 132 4 Law Law NNP cord-326740-1fjr9qr4 132 5 , , , cord-326740-1fjr9qr4 132 6 the the DT cord-326740-1fjr9qr4 132 7 mean mean NN cord-326740-1fjr9qr4 132 8 waiting wait VBG cord-326740-1fjr9qr4 132 9 λ λ NN cord-326740-1fjr9qr4 132 10 time time NN cord-326740-1fjr9qr4 132 11 outside outside IN cord-326740-1fjr9qr4 132 12 the the DT cord-326740-1fjr9qr4 132 13 store store NN cord-326740-1fjr9qr4 132 14 is be VBZ cord-326740-1fjr9qr4 132 15 . . . cord-326740-1fjr9qr4 133 1 The the DT cord-326740-1fjr9qr4 133 2 mean mean NN cord-326740-1fjr9qr4 133 3 waiting wait VBG cord-326740-1fjr9qr4 133 4 time time NN cord-326740-1fjr9qr4 133 5 at at IN cord-326740-1fjr9qr4 133 6 the the DT cord-326740-1fjr9qr4 133 7 shopping shopping NN cord-326740-1fjr9qr4 133 8 area area NN cord-326740-1fjr9qr4 133 9 is be VBZ cord-326740-1fjr9qr4 133 10 and and CC cord-326740-1fjr9qr4 133 11 the the DT cord-326740-1fjr9qr4 133 12 mean mean JJ cord-326740-1fjr9qr4 133 13 waiting wait VBG cord-326740-1fjr9qr4 133 14 time time NN cord-326740-1fjr9qr4 133 15 at at IN cord-326740-1fjr9qr4 133 16 the the DT cord-326740-1fjr9qr4 133 17 payer payer NN cord-326740-1fjr9qr4 133 18 area area NN cord-326740-1fjr9qr4 133 19 is be VBZ cord-326740-1fjr9qr4 134 1 We -PRON- PRP cord-326740-1fjr9qr4 134 2 next next RB cord-326740-1fjr9qr4 134 3 study study VBP cord-326740-1fjr9qr4 134 4 the the DT cord-326740-1fjr9qr4 134 5 effect effect NN cord-326740-1fjr9qr4 134 6 of of IN cord-326740-1fjr9qr4 134 7 the the DT cord-326740-1fjr9qr4 134 8 two two CD cord-326740-1fjr9qr4 134 9 models model NNS cord-326740-1fjr9qr4 134 10 ' ' POS cord-326740-1fjr9qr4 134 11 parameters parameter NNS cord-326740-1fjr9qr4 134 12 on on IN cord-326740-1fjr9qr4 134 13 the the DT cord-326740-1fjr9qr4 134 14 performance performance NN cord-326740-1fjr9qr4 134 15 measures measure NNS cord-326740-1fjr9qr4 134 16 . . . cord-326740-1fjr9qr4 135 1 Let let VB cord-326740-1fjr9qr4 135 2 the the DT cord-326740-1fjr9qr4 135 3 arrival arrival NN cord-326740-1fjr9qr4 135 4 rate rate NN cord-326740-1fjr9qr4 135 5 , , , cord-326740-1fjr9qr4 135 6 service service NN cord-326740-1fjr9qr4 135 7 rate rate NN cord-326740-1fjr9qr4 135 8 , , , cord-326740-1fjr9qr4 135 9 and and CC cord-326740-1fjr9qr4 135 10 shopping shopping NN cord-326740-1fjr9qr4 135 11 rate rate NN cord-326740-1fjr9qr4 135 12 , , , cord-326740-1fjr9qr4 135 13 respectively respectively RB cord-326740-1fjr9qr4 135 14 , , , cord-326740-1fjr9qr4 135 15 be be VB cord-326740-1fjr9qr4 135 16 customers customer NNS cord-326740-1fjr9qr4 135 17 λ λ NNP cord-326740-1fjr9qr4 135 18 18 18 CD cord-326740-1fjr9qr4 135 19 , , , cord-326740-1fjr9qr4 135 20 μ μ NN cord-326740-1fjr9qr4 135 21 10 10 CD cord-326740-1fjr9qr4 135 22 , , , cord-326740-1fjr9qr4 135 23 and and CC cord-326740-1fjr9qr4 135 24 3 3 CD cord-326740-1fjr9qr4 136 1   NNP cord-326740-1fjr9qr4 136 2   NNPS cord-326740-1fjr9qr4 137 1   NNS cord-326740-1fjr9qr4 137 2   NNS cord-326740-1fjr9qr4 137 3 per per IN cord-326740-1fjr9qr4 137 4 hour hour NN cord-326740-1fjr9qr4 137 5 . . . cord-326740-1fjr9qr4 138 1 Set Set NNP cord-326740-1fjr9qr4 138 2 M M NNP cord-326740-1fjr9qr4 138 3 = = SYM cord-326740-1fjr9qr4 138 4 15 15 CD cord-326740-1fjr9qr4 138 5 , , , cord-326740-1fjr9qr4 138 6 N n CD cord-326740-1fjr9qr4 138 7 = = SYM cord-326740-1fjr9qr4 138 8 5 5 CD cord-326740-1fjr9qr4 138 9 , , , cord-326740-1fjr9qr4 138 10 and and CC cord-326740-1fjr9qr4 138 11 c c NN cord-326740-1fjr9qr4 138 12 = = SYM cord-326740-1fjr9qr4 138 13 2 2 CD cord-326740-1fjr9qr4 138 14 so so IN cord-326740-1fjr9qr4 138 15 that that IN cord-326740-1fjr9qr4 138 16 the the DT cord-326740-1fjr9qr4 138 17 maximum maximum JJ cord-326740-1fjr9qr4 138 18 number number NN cord-326740-1fjr9qr4 138 19 of of IN cord-326740-1fjr9qr4 138 20 customers customer NNS cord-326740-1fjr9qr4 138 21 in in IN cord-326740-1fjr9qr4 138 22 the the DT cord-326740-1fjr9qr4 138 23 shopping shopping NN cord-326740-1fjr9qr4 138 24 area area NN cord-326740-1fjr9qr4 138 25 is be VBZ cord-326740-1fjr9qr4 138 26 For for IN cord-326740-1fjr9qr4 138 27 these these DT cord-326740-1fjr9qr4 138 28 values value NNS cord-326740-1fjr9qr4 138 29 , , , cord-326740-1fjr9qr4 138 30 the the DT cord-326740-1fjr9qr4 138 31 right right JJ cord-326740-1fjr9qr4 138 32 - - HYPH cord-326740-1fjr9qr4 138 33 hand hand NN cord-326740-1fjr9qr4 138 34 side side NN cord-326740-1fjr9qr4 138 35 of of IN cord-326740-1fjr9qr4 138 36 the the DT cord-326740-1fjr9qr4 138 37 stability stability NN cord-326740-1fjr9qr4 138 38 condition condition NN cord-326740-1fjr9qr4 138 39 is be VBZ cord-326740-1fjr9qr4 138 40 15 15 CD cord-326740-1fjr9qr4 138 41 5 5 CD cord-326740-1fjr9qr4 138 42 2 2 CD cord-326740-1fjr9qr4 138 43 8 8 CD cord-326740-1fjr9qr4 138 44 . . . cord-326740-1fjr9qr4 139 1 cashiers cashier NNS cord-326740-1fjr9qr4 139 2 increases increase VBZ cord-326740-1fjr9qr4 139 3 the the DT cord-326740-1fjr9qr4 139 4 service service NN cord-326740-1fjr9qr4 139 5 rate rate NN cord-326740-1fjr9qr4 139 6 at at IN cord-326740-1fjr9qr4 139 7 the the DT cord-326740-1fjr9qr4 139 8 payment payment NN cord-326740-1fjr9qr4 139 9 area area NN cord-326740-1fjr9qr4 139 10 . . . cord-326740-1fjr9qr4 140 1 Customers customer NNS cord-326740-1fjr9qr4 140 2 can can MD cord-326740-1fjr9qr4 140 3 proceed proceed VB cord-326740-1fjr9qr4 140 4 more more RBR cord-326740-1fjr9qr4 140 5 rapidly rapidly RB cord-326740-1fjr9qr4 140 6 through through IN cord-326740-1fjr9qr4 140 7 the the DT cord-326740-1fjr9qr4 140 8 payment payment NN cord-326740-1fjr9qr4 140 9 phase phase NN cord-326740-1fjr9qr4 140 10 , , , cord-326740-1fjr9qr4 140 11 reducing reduce VBG cord-326740-1fjr9qr4 140 12 the the DT cord-326740-1fjr9qr4 140 13 amount amount NN cord-326740-1fjr9qr4 140 14 of of IN cord-326740-1fjr9qr4 140 15 time time NN cord-326740-1fjr9qr4 140 16 spent spend VBN cord-326740-1fjr9qr4 140 17 waiting wait VBG cord-326740-1fjr9qr4 140 18 in in IN cord-326740-1fjr9qr4 140 19 the the DT cord-326740-1fjr9qr4 140 20 designated designated JJ cord-326740-1fjr9qr4 140 21 area area NN cord-326740-1fjr9qr4 140 22 and and CC cord-326740-1fjr9qr4 140 23 reducing reduce VBG cord-326740-1fjr9qr4 140 24 the the DT cord-326740-1fjr9qr4 140 25 number number NN cord-326740-1fjr9qr4 140 26 of of IN cord-326740-1fjr9qr4 140 27 customers customer NNS cord-326740-1fjr9qr4 140 28 who who WP cord-326740-1fjr9qr4 140 29 must must MD cord-326740-1fjr9qr4 140 30 orbit orbit VB cord-326740-1fjr9qr4 140 31 in in IN cord-326740-1fjr9qr4 140 32 the the DT cord-326740-1fjr9qr4 140 33 shopping shopping NN cord-326740-1fjr9qr4 140 34 area area NN cord-326740-1fjr9qr4 140 35 . . . cord-326740-1fjr9qr4 141 1 The the DT cord-326740-1fjr9qr4 141 2 smallest small JJS cord-326740-1fjr9qr4 141 3 value value NN cord-326740-1fjr9qr4 141 4 of of IN cord-326740-1fjr9qr4 141 5 N n NN cord-326740-1fjr9qr4 141 6 ( ( -LRB- cord-326740-1fjr9qr4 141 7 the the DT cord-326740-1fjr9qr4 141 8 number number NN cord-326740-1fjr9qr4 141 9 of of IN cord-326740-1fjr9qr4 141 10 payers payer NNS cord-326740-1fjr9qr4 141 11 who who WP cord-326740-1fjr9qr4 141 12 can can MD cord-326740-1fjr9qr4 141 13 occupy occupy VB cord-326740-1fjr9qr4 141 14 the the DT cord-326740-1fjr9qr4 141 15 payment payment NN cord-326740-1fjr9qr4 141 16 space space NN cord-326740-1fjr9qr4 141 17 ) ) -RRB- cord-326740-1fjr9qr4 141 18 that that WDT cord-326740-1fjr9qr4 141 19 sustains sustain VBZ cord-326740-1fjr9qr4 141 20 the the DT cord-326740-1fjr9qr4 141 21 stability stability NN cord-326740-1fjr9qr4 141 22 condition condition NN cord-326740-1fjr9qr4 141 23 is be VBZ cord-326740-1fjr9qr4 141 24 4 4 CD cord-326740-1fjr9qr4 141 25 . . . cord-326740-1fjr9qr4 142 1 When when WRB cord-326740-1fjr9qr4 142 2 the the DT cord-326740-1fjr9qr4 142 3 value value NN cord-326740-1fjr9qr4 142 4 of of IN cord-326740-1fjr9qr4 142 5 N n CD cord-326740-1fjr9qr4 142 6 increases increase NNS cord-326740-1fjr9qr4 142 7 , , , cord-326740-1fjr9qr4 142 8 as as IN cord-326740-1fjr9qr4 142 9 depicted depict VBN cord-326740-1fjr9qr4 142 10 in in IN cord-326740-1fjr9qr4 142 11 Figure figure NN cord-326740-1fjr9qr4 142 12 11b 11b NNS cord-326740-1fjr9qr4 142 13 , , , cord-326740-1fjr9qr4 142 14 OUT out NN cord-326740-1fjr9qr4 142 15 E E NNP cord-326740-1fjr9qr4 142 16 W W NNP cord-326740-1fjr9qr4 142 17 Several several JJ cord-326740-1fjr9qr4 142 18 studies study NNS cord-326740-1fjr9qr4 142 19 have have VBP cord-326740-1fjr9qr4 142 20 adopted adopt VBN cord-326740-1fjr9qr4 142 21 game game NN cord-326740-1fjr9qr4 142 22 - - HYPH cord-326740-1fjr9qr4 142 23 theoretic theoretic JJ cord-326740-1fjr9qr4 142 24 approaches approach NNS cord-326740-1fjr9qr4 142 25 when when WRB cord-326740-1fjr9qr4 142 26 analyzing analyze VBG cord-326740-1fjr9qr4 142 27 safety safety NN cord-326740-1fjr9qr4 142 28 - - HYPH cord-326740-1fjr9qr4 142 29 related relate VBN cord-326740-1fjr9qr4 142 30 events event NNS cord-326740-1fjr9qr4 142 31 ( ( -LRB- cord-326740-1fjr9qr4 142 32 see see VB cord-326740-1fjr9qr4 142 33 Winkler Winkler NNP cord-326740-1fjr9qr4 142 34 et et NNP cord-326740-1fjr9qr4 142 35 al al NNP cord-326740-1fjr9qr4 142 36 . . . cord-326740-1fjr9qr4 143 1 ( ( -LRB- cord-326740-1fjr9qr4 143 2 2019 2019 CD cord-326740-1fjr9qr4 143 3 ) ) -RRB- cord-326740-1fjr9qr4 143 4 for for IN cord-326740-1fjr9qr4 143 5 a a DT cord-326740-1fjr9qr4 143 6 review review NN cord-326740-1fjr9qr4 143 7 ) ) -RRB- cord-326740-1fjr9qr4 143 8 . . . cord-326740-1fjr9qr4 144 1 We -PRON- PRP cord-326740-1fjr9qr4 144 2 construct construct VBP cord-326740-1fjr9qr4 144 3 and and CC cord-326740-1fjr9qr4 144 4 analyze analyze VB cord-326740-1fjr9qr4 144 5 a a DT cord-326740-1fjr9qr4 144 6 COVID-19 covid-19 JJ cord-326740-1fjr9qr4 144 7 queueing queueing NN cord-326740-1fjr9qr4 144 8 game game NN cord-326740-1fjr9qr4 144 9 between between IN cord-326740-1fjr9qr4 144 10 the the DT cord-326740-1fjr9qr4 144 11 authority authority NN cord-326740-1fjr9qr4 144 12 aiming aim VBG cord-326740-1fjr9qr4 144 13 to to TO cord-326740-1fjr9qr4 144 14 reduce reduce VB cord-326740-1fjr9qr4 144 15 the the DT cord-326740-1fjr9qr4 144 16 risk risk NN cord-326740-1fjr9qr4 144 17 of of IN cord-326740-1fjr9qr4 144 18 infection infection NN cord-326740-1fjr9qr4 144 19 while while IN cord-326740-1fjr9qr4 144 20 keeping keep VBG cord-326740-1fjr9qr4 144 21 customers customer NNS cord-326740-1fjr9qr4 144 22 and and CC cord-326740-1fjr9qr4 144 23 workers worker NNS cord-326740-1fjr9qr4 144 24 safe safe JJ cord-326740-1fjr9qr4 144 25 and and CC cord-326740-1fjr9qr4 144 26 a a DT cord-326740-1fjr9qr4 144 27 businesses business NNS cord-326740-1fjr9qr4 144 28 that that WDT cord-326740-1fjr9qr4 144 29 wants want VBZ cord-326740-1fjr9qr4 144 30 to to TO cord-326740-1fjr9qr4 144 31 minimize minimize VB cord-326740-1fjr9qr4 144 32 its -PRON- PRP$ cord-326740-1fjr9qr4 144 33 costs cost NNS cord-326740-1fjr9qr4 144 34 . . . cord-326740-1fjr9qr4 145 1 Specifically specifically RB cord-326740-1fjr9qr4 145 2 , , , cord-326740-1fjr9qr4 145 3 the the DT cord-326740-1fjr9qr4 145 4 authority authority NN cord-326740-1fjr9qr4 145 5 chooses choose VBZ cord-326740-1fjr9qr4 145 6 the the DT cord-326740-1fjr9qr4 145 7 maximum maximum JJ cord-326740-1fjr9qr4 145 8 number number NN cord-326740-1fjr9qr4 145 9 of of IN cord-326740-1fjr9qr4 145 10 customers customer NNS cord-326740-1fjr9qr4 145 11 allowed allow VBN cord-326740-1fjr9qr4 145 12 in in IN cord-326740-1fjr9qr4 145 13 the the DT cord-326740-1fjr9qr4 145 14 store store NN cord-326740-1fjr9qr4 145 15 , , , cord-326740-1fjr9qr4 145 16 M. M. NNP cord-326740-1fjr9qr4 146 1 The the DT cord-326740-1fjr9qr4 146 2 objective objective NN cord-326740-1fjr9qr4 146 3 of of IN cord-326740-1fjr9qr4 146 4 the the DT cord-326740-1fjr9qr4 146 5 authority authority NN cord-326740-1fjr9qr4 146 6 is be VBZ cord-326740-1fjr9qr4 146 7 ( ( -LRB- cord-326740-1fjr9qr4 146 8 9 9 CD cord-326740-1fjr9qr4 146 9 ) ) -RRB- cord-326740-1fjr9qr4 146 10   . cord-326740-1fjr9qr4 147 1   NNP cord-326740-1fjr9qr4 147 2 _SP cord-326740-1fjr9qr4 148 1 where where WRB cord-326740-1fjr9qr4 148 2 denotes denote VBZ cord-326740-1fjr9qr4 148 3 the the DT cord-326740-1fjr9qr4 148 4 weight weight NN cord-326740-1fjr9qr4 148 5 the the DT cord-326740-1fjr9qr4 148 6 authority authority NN cord-326740-1fjr9qr4 148 7 assigns assign VBZ cord-326740-1fjr9qr4 148 8 to to IN cord-326740-1fjr9qr4 148 9 each each DT cord-326740-1fjr9qr4 148 10 measure measure NN cord-326740-1fjr9qr4 148 11 of of IN cord-326740-1fjr9qr4 148 12 risk risk NN cord-326740-1fjr9qr4 148 13 . . . cord-326740-1fjr9qr4 149 1 It -PRON- PRP cord-326740-1fjr9qr4 149 2 is be VBZ cord-326740-1fjr9qr4 149 3 reasonable reasonable JJ cord-326740-1fjr9qr4 149 4 to to IN cord-326740-1fjr9qr4 149 5 α α NN cord-326740-1fjr9qr4 149 6 i i PRP cord-326740-1fjr9qr4 149 7 assume assume VBP cord-326740-1fjr9qr4 149 8 that that IN cord-326740-1fjr9qr4 149 9 the the DT cord-326740-1fjr9qr4 149 10 authority authority NN cord-326740-1fjr9qr4 149 11 assigns assign VBZ cord-326740-1fjr9qr4 149 12 a a DT cord-326740-1fjr9qr4 149 13 smaller small JJR cord-326740-1fjr9qr4 149 14 weight weight NN cord-326740-1fjr9qr4 149 15 to to IN cord-326740-1fjr9qr4 149 16 queues queue NNS cord-326740-1fjr9qr4 149 17 forming form VBG cord-326740-1fjr9qr4 149 18 outside outside IN cord-326740-1fjr9qr4 149 19 a a DT cord-326740-1fjr9qr4 149 20 store store NN cord-326740-1fjr9qr4 149 21 ; ; : cord-326740-1fjr9qr4 149 22 therefore therefore RB cord-326740-1fjr9qr4 149 23 , , , cord-326740-1fjr9qr4 149 24 in in IN cord-326740-1fjr9qr4 149 25 this this DT cord-326740-1fjr9qr4 149 26 case case NN cord-326740-1fjr9qr4 149 27 , , , cord-326740-1fjr9qr4 149 28 receives receive VBZ cord-326740-1fjr9qr4 149 29 the the DT cord-326740-1fjr9qr4 149 30 smallest small JJS cord-326740-1fjr9qr4 149 31 weighting weighting NN cord-326740-1fjr9qr4 149 32 . . . cord-326740-1fjr9qr4 150 1 Store store NN cord-326740-1fjr9qr4 150 2 management management NN cord-326740-1fjr9qr4 150 3 can can MD cord-326740-1fjr9qr4 150 4 not not RB cord-326740-1fjr9qr4 150 5 exceed exceed VB cord-326740-1fjr9qr4 150 6 the the DT cord-326740-1fjr9qr4 150 7 limit limit NN cord-326740-1fjr9qr4 150 8 set set VBN cord-326740-1fjr9qr4 150 9 by by IN cord-326740-1fjr9qr4 150 10 The the DT cord-326740-1fjr9qr4 150 11 store store NN cord-326740-1fjr9qr4 150 12 's 's POS cord-326740-1fjr9qr4 150 13 equilibrium equilibrium NN cord-326740-1fjr9qr4 150 14 strategy strategy NN cord-326740-1fjr9qr4 150 15 also also RB cord-326740-1fjr9qr4 150 16 depends depend VBZ cord-326740-1fjr9qr4 150 17 on on IN cord-326740-1fjr9qr4 150 18 the the DT cord-326740-1fjr9qr4 150 19 values value NNS cord-326740-1fjr9qr4 150 20 of of IN cord-326740-1fjr9qr4 150 21 the the DT cord-326740-1fjr9qr4 150 22 weights weight NNS cord-326740-1fjr9qr4 150 23 assigned assign VBN cord-326740-1fjr9qr4 150 24 by by IN cord-326740-1fjr9qr4 150 25 the the DT cord-326740-1fjr9qr4 150 26 authority authority NN cord-326740-1fjr9qr4 150 27 to to IN cord-326740-1fjr9qr4 150 28 each each DT cord-326740-1fjr9qr4 150 29 measure measure NN cord-326740-1fjr9qr4 150 30 of of IN cord-326740-1fjr9qr4 150 31 risk risk NN cord-326740-1fjr9qr4 150 32 . . . cord-326740-1fjr9qr4 151 1 Set Set VBN cord-326740-1fjr9qr4 151 2 . . . cord-326740-1fjr9qr4 152 1 These these DT cord-326740-1fjr9qr4 152 2 weights weight NNS cord-326740-1fjr9qr4 152 3 reflect reflect VBP cord-326740-1fjr9qr4 152 4 the the DT cord-326740-1fjr9qr4 152 5 ICU ICU NNP cord-326740-1fjr9qr4 152 6 capacity capacity NN cord-326740-1fjr9qr4 152 7 management management NN cord-326740-1fjr9qr4 152 8 during during IN cord-326740-1fjr9qr4 152 9 the the DT cord-326740-1fjr9qr4 152 10 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 152 11 pandemic pandemic NN cord-326740-1fjr9qr4 152 12 using use VBG cord-326740-1fjr9qr4 152 13 a a DT cord-326740-1fjr9qr4 152 14 stochastic stochastic JJ cord-326740-1fjr9qr4 152 15 process process NN cord-326740-1fjr9qr4 152 16 simulation simulation NN cord-326740-1fjr9qr4 152 17 A a DT cord-326740-1fjr9qr4 152 18 retrial retrial NN cord-326740-1fjr9qr4 152 19 system system NN cord-326740-1fjr9qr4 152 20 with with IN cord-326740-1fjr9qr4 152 21 two two CD cord-326740-1fjr9qr4 152 22 input input NN cord-326740-1fjr9qr4 152 23 streams stream NNS cord-326740-1fjr9qr4 152 24 and and CC cord-326740-1fjr9qr4 152 25 two two CD cord-326740-1fjr9qr4 152 26 orbit orbit NN cord-326740-1fjr9qr4 152 27 queues queue NNS cord-326740-1fjr9qr4 152 28 The the DT cord-326740-1fjr9qr4 152 29 Covid-19 Covid-19 NNP cord-326740-1fjr9qr4 152 30 Crisis Crisis NNP cord-326740-1fjr9qr4 152 31 and and CC cord-326740-1fjr9qr4 152 32 the the DT cord-326740-1fjr9qr4 152 33 need need NN cord-326740-1fjr9qr4 152 34 for for IN cord-326740-1fjr9qr4 152 35 suitable suitable JJ cord-326740-1fjr9qr4 152 36 face face NN cord-326740-1fjr9qr4 152 37 masks mask NNS cord-326740-1fjr9qr4 152 38 for for IN cord-326740-1fjr9qr4 152 39 the the DT cord-326740-1fjr9qr4 152 40 general general JJ cord-326740-1fjr9qr4 152 41 population population NN cord-326740-1fjr9qr4 152 42 Keeping keep VBG cord-326740-1fjr9qr4 152 43 Workers Workers NNPS cord-326740-1fjr9qr4 152 44 and and CC cord-326740-1fjr9qr4 152 45 Customers customer NNS cord-326740-1fjr9qr4 152 46 Safe safe JJ cord-326740-1fjr9qr4 152 47 during during IN cord-326740-1fjr9qr4 152 48 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 152 49 in in IN cord-326740-1fjr9qr4 152 50 Restaurants restaurant NNS cord-326740-1fjr9qr4 152 51 Enabling enable VBG cord-326740-1fjr9qr4 152 52 and and CC cord-326740-1fjr9qr4 152 53 enforcing enforce VBG cord-326740-1fjr9qr4 152 54 social social JJ cord-326740-1fjr9qr4 152 55 distancing distance VBG cord-326740-1fjr9qr4 152 56 measures measure NNS cord-326740-1fjr9qr4 152 57 using use VBG cord-326740-1fjr9qr4 152 58 smart smart JJ cord-326740-1fjr9qr4 152 59 city city NN cord-326740-1fjr9qr4 152 60 and and CC cord-326740-1fjr9qr4 152 61 its -PRON- PRP$ cord-326740-1fjr9qr4 152 62 infrastructures infrastructure NNS cord-326740-1fjr9qr4 152 63 : : : cord-326740-1fjr9qr4 152 64 a a DT cord-326740-1fjr9qr4 152 65 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 152 66 Use Use NNP cord-326740-1fjr9qr4 152 67 case case NN cord-326740-1fjr9qr4 152 68 Explicit Explicit NNP cord-326740-1fjr9qr4 152 69 Solutions Solutions NNPS cord-326740-1fjr9qr4 152 70 for for IN cord-326740-1fjr9qr4 152 71 Continuous Continuous NNP cord-326740-1fjr9qr4 152 72 - - HYPH cord-326740-1fjr9qr4 152 73 Time Time NNP cord-326740-1fjr9qr4 152 74 QBD qbd NN cord-326740-1fjr9qr4 152 75 Processes process NNS cord-326740-1fjr9qr4 152 76 by by IN cord-326740-1fjr9qr4 152 77 Using use VBG cord-326740-1fjr9qr4 152 78 Relations Relations NNPS cord-326740-1fjr9qr4 152 79 Between between IN cord-326740-1fjr9qr4 152 80 Matrix Matrix NNP cord-326740-1fjr9qr4 152 81 Geometric Geometric NNP cord-326740-1fjr9qr4 152 82 Analysis Analysis NNP cord-326740-1fjr9qr4 152 83 and and CC cord-326740-1fjr9qr4 152 84 the the DT cord-326740-1fjr9qr4 152 85 Probability Probability NNP cord-326740-1fjr9qr4 152 86 Generating Generating NNP cord-326740-1fjr9qr4 152 87 Functions Functions NNPS cord-326740-1fjr9qr4 152 88 Method Method NNP cord-326740-1fjr9qr4 152 89 Performance performance NN cord-326740-1fjr9qr4 152 90 modeling modeling NN cord-326740-1fjr9qr4 152 91 and and CC cord-326740-1fjr9qr4 152 92 design design NN cord-326740-1fjr9qr4 152 93 of of IN cord-326740-1fjr9qr4 152 94 computer computer NN cord-326740-1fjr9qr4 152 95 systems system NNS cord-326740-1fjr9qr4 152 96 : : : cord-326740-1fjr9qr4 152 97 queueing queue VBG cord-326740-1fjr9qr4 152 98 theory theory NN cord-326740-1fjr9qr4 152 99 in in IN cord-326740-1fjr9qr4 152 100 action action NN cord-326740-1fjr9qr4 152 101 OM OM NNP cord-326740-1fjr9qr4 152 102 Forum Forum NNP cord-326740-1fjr9qr4 152 103 - - HYPH cord-326740-1fjr9qr4 152 104 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 152 105 Scratch Scratch NNP cord-326740-1fjr9qr4 152 106 Models Models NNPS cord-326740-1fjr9qr4 152 107 to to TO cord-326740-1fjr9qr4 152 108 Support support VB cord-326740-1fjr9qr4 152 109 Local local JJ cord-326740-1fjr9qr4 152 110 Decisions Decisions NNPS cord-326740-1fjr9qr4 152 111 Pooling Pooling NNP cord-326740-1fjr9qr4 152 112 and and CC cord-326740-1fjr9qr4 152 113 Balking balking NN cord-326740-1fjr9qr4 152 114 : : : cord-326740-1fjr9qr4 152 115 Decisions decision NNS cord-326740-1fjr9qr4 152 116 on on IN cord-326740-1fjr9qr4 152 117 COVID-19 covid-19 NN cord-326740-1fjr9qr4 152 118 Available available JJ cord-326740-1fjr9qr4 152 119 at at IN cord-326740-1fjr9qr4 152 120 SSRN SSRN NNP cord-326740-1fjr9qr4 152 121 3628484 3628484 CD cord-326740-1fjr9qr4 153 1 The the DT cord-326740-1fjr9qr4 153 2 Israeli israeli JJ cord-326740-1fjr9qr4 153 3 queue queue NN cord-326740-1fjr9qr4 153 4 with with IN cord-326740-1fjr9qr4 153 5 retrials retrial NNS cord-326740-1fjr9qr4 153 6 On on IN cord-326740-1fjr9qr4 153 7 tandem tandem JJ cord-326740-1fjr9qr4 153 8 stochastic stochastic JJ cord-326740-1fjr9qr4 153 9 networks network NNS cord-326740-1fjr9qr4 153 10 with with IN cord-326740-1fjr9qr4 153 11 time time NN cord-326740-1fjr9qr4 153 12 - - HYPH cord-326740-1fjr9qr4 153 13 deteriorating deteriorate VBG cord-326740-1fjr9qr4 153 14 product product NN cord-326740-1fjr9qr4 153 15 quality quality NN cord-326740-1fjr9qr4 153 16 Reporting report VBG cord-326740-1fjr9qr4 153 17 near near RB cord-326740-1fjr9qr4 153 18 - - HYPH cord-326740-1fjr9qr4 153 19 miss miss NN cord-326740-1fjr9qr4 153 20 safety safety NN cord-326740-1fjr9qr4 153 21 events event NNS cord-326740-1fjr9qr4 153 22 : : : cord-326740-1fjr9qr4 154 1 Impacts impact NNS cord-326740-1fjr9qr4 154 2 and and CC cord-326740-1fjr9qr4 154 3 decision decision NN cord-326740-1fjr9qr4 154 4 - - HYPH cord-326740-1fjr9qr4 154 5 making make VBG cord-326740-1fjr9qr4 154 6 analysis analysis NN cord-326740-1fjr9qr4 155 1 In in IN cord-326740-1fjr9qr4 155 2 this this DT cord-326740-1fjr9qr4 155 3 paper paper NN cord-326740-1fjr9qr4 155 4 , , , cord-326740-1fjr9qr4 155 5 we -PRON- PRP cord-326740-1fjr9qr4 155 6 construct construct VBP cord-326740-1fjr9qr4 155 7 and and CC cord-326740-1fjr9qr4 155 8 analyze analyze VB cord-326740-1fjr9qr4 155 9 two two CD cord-326740-1fjr9qr4 155 10 special special JJ cord-326740-1fjr9qr4 155 11 nonclassical nonclassical JJ cord-326740-1fjr9qr4 155 12 multi multi JJ cord-326740-1fjr9qr4 155 13 - - JJ cord-326740-1fjr9qr4 155 14 server server JJ cord-326740-1fjr9qr4 155 15 queueing queueing NN cord-326740-1fjr9qr4 155 16 models model NNS cord-326740-1fjr9qr4 155 17 to to TO cord-326740-1fjr9qr4 155 18 control control VB cord-326740-1fjr9qr4 155 19 queueing queueing NN cord-326740-1fjr9qr4 155 20 problems problem NNS cord-326740-1fjr9qr4 155 21 generated generate VBN cord-326740-1fjr9qr4 155 22 by by IN cord-326740-1fjr9qr4 155 23 social social JJ cord-326740-1fjr9qr4 155 24 distancing distance VBG cord-326740-1fjr9qr4 155 25 constraints constraint NNS cord-326740-1fjr9qr4 155 26 associated associate VBN cord-326740-1fjr9qr4 155 27 with with IN cord-326740-1fjr9qr4 155 28 the the DT cord-326740-1fjr9qr4 155 29 COVID-19 COVID-19 NNP cord-326740-1fjr9qr4 155 30 pandemic pandemic NN cord-326740-1fjr9qr4 155 31 such such JJ cord-326740-1fjr9qr4 155 32 as as IN cord-326740-1fjr9qr4 155 33 " " `` cord-326740-1fjr9qr4 155 34 Maximum maximum JJ cord-326740-1fjr9qr4 155 35 shoppers shopper NNS cord-326740-1fjr9qr4 155 36 at at IN cord-326740-1fjr9qr4 155 37 store store NN cord-326740-1fjr9qr4 155 38 " " '' cord-326740-1fjr9qr4 155 39 and and CC cord-326740-1fjr9qr4 155 40 " " `` cord-326740-1fjr9qr4 155 41 maximum maximum JJ cord-326740-1fjr9qr4 155 42 number number NN cord-326740-1fjr9qr4 155 43 of of IN cord-326740-1fjr9qr4 155 44 customers customer NNS cord-326740-1fjr9qr4 155 45 in in IN cord-326740-1fjr9qr4 155 46 checkout checkout NN cord-326740-1fjr9qr4 155 47 area area NN cord-326740-1fjr9qr4 155 48 . . . cord-326740-1fjr9qr4 155 49 " " '' cord-326740-1fjr9qr4 156 1 In in IN cord-326740-1fjr9qr4 156 2 both both DT cord-326740-1fjr9qr4 156 3 models model NNS cord-326740-1fjr9qr4 156 4 , , , cord-326740-1fjr9qr4 156 5 a a DT cord-326740-1fjr9qr4 156 6 capacity capacity NN cord-326740-1fjr9qr4 156 7 constraint constraint NN cord-326740-1fjr9qr4 156 8 is be VBZ cord-326740-1fjr9qr4 156 9 imposed impose VBN cord-326740-1fjr9qr4 156 10 that that WDT cord-326740-1fjr9qr4 156 11 limits limit VBZ cord-326740-1fjr9qr4 156 12 the the DT cord-326740-1fjr9qr4 156 13 number number NN cord-326740-1fjr9qr4 156 14 of of IN cord-326740-1fjr9qr4 156 15 customers customer NNS cord-326740-1fjr9qr4 156 16 allowed allow VBN cord-326740-1fjr9qr4 156 17 inside inside IN cord-326740-1fjr9qr4 156 18 the the DT cord-326740-1fjr9qr4 156 19 store store NN cord-326740-1fjr9qr4 156 20 at at IN cord-326740-1fjr9qr4 156 21 one one CD cord-326740-1fjr9qr4 156 22 time time NN cord-326740-1fjr9qr4 156 23 . . . cord-326740-1fjr9qr4 157 1 The the DT cord-326740-1fjr9qr4 157 2 governing govern VBG cord-326740-1fjr9qr4 157 3 authority authority NN cord-326740-1fjr9qr4 157 4 that that WDT cord-326740-1fjr9qr4 157 5 imposes impose VBZ cord-326740-1fjr9qr4 157 6 the the DT cord-326740-1fjr9qr4 157 7 limit limit NN cord-326740-1fjr9qr4 157 8 acts act VBZ cord-326740-1fjr9qr4 157 9 as as IN cord-326740-1fjr9qr4 157 10 a a DT cord-326740-1fjr9qr4 157 11 Stackelberg Stackelberg NNP cord-326740-1fjr9qr4 157 12 leader leader NN cord-326740-1fjr9qr4 157 13 in in IN cord-326740-1fjr9qr4 157 14 choosing choose VBG cord-326740-1fjr9qr4 157 15 how how WRB cord-326740-1fjr9qr4 157 16 many many JJ cord-326740-1fjr9qr4 157 17 customers customer NNS cord-326740-1fjr9qr4 157 18 will will MD cord-326740-1fjr9qr4 157 19 be be VB cord-326740-1fjr9qr4 157 20 allowed allow VBN cord-326740-1fjr9qr4 157 21 . . . cord-326740-1fjr9qr4 158 1 Then then RB cord-326740-1fjr9qr4 158 2 , , , cord-326740-1fjr9qr4 158 3 store store NN cord-326740-1fjr9qr4 158 4 management management NN cord-326740-1fjr9qr4 158 5 chooses choose VBZ cord-326740-1fjr9qr4 158 6 the the DT cord-326740-1fjr9qr4 158 7 number number NN cord-326740-1fjr9qr4 158 8 of of IN cord-326740-1fjr9qr4 158 9 cashiers cashier NNS cord-326740-1fjr9qr4 158 10 to to TO cord-326740-1fjr9qr4 158 11 employ employ VB cord-326740-1fjr9qr4 158 12 to to TO cord-326740-1fjr9qr4 158 13 reduce reduce VB cord-326740-1fjr9qr4 158 14 its -PRON- PRP$ cord-326740-1fjr9qr4 158 15 costs cost NNS cord-326740-1fjr9qr4 158 16 in in IN cord-326740-1fjr9qr4 158 17 terms term NNS cord-326740-1fjr9qr4 158 18 of of IN cord-326740-1fjr9qr4 158 19 cashier cashier NN cord-326740-1fjr9qr4 158 20 salaries salary NNS cord-326740-1fjr9qr4 158 21 and and CC cord-326740-1fjr9qr4 158 22 the the DT cord-326740-1fjr9qr4 158 23 cost cost NN cord-326740-1fjr9qr4 158 24 of of IN cord-326740-1fjr9qr4 158 25 dissatisfaction dissatisfaction NN cord-326740-1fjr9qr4 158 26 from from IN cord-326740-1fjr9qr4 158 27 customers customer NNS cord-326740-1fjr9qr4 158 28 waiting wait VBG cord-326740-1fjr9qr4 158 29 in in IN cord-326740-1fjr9qr4 158 30 line line NN cord-326740-1fjr9qr4 158 31 . . . cord-326740-1fjr9qr4 159 1 In in IN cord-326740-1fjr9qr4 159 2 the the DT cord-326740-1fjr9qr4 159 3 second second JJ cord-326740-1fjr9qr4 159 4 model model NN cord-326740-1fjr9qr4 159 5 , , , cord-326740-1fjr9qr4 159 6 store store NN cord-326740-1fjr9qr4 159 7 management management NN cord-326740-1fjr9qr4 159 8 can can MD cord-326740-1fjr9qr4 159 9 also also RB cord-326740-1fjr9qr4 159 10 choose choose VB cord-326740-1fjr9qr4 159 11 a a DT cord-326740-1fjr9qr4 159 12 maximum maximum JJ cord-326740-1fjr9qr4 159 13 number number NN cord-326740-1fjr9qr4 159 14 of of IN cord-326740-1fjr9qr4 159 15 customers customer NNS cord-326740-1fjr9qr4 159 16 who who WP cord-326740-1fjr9qr4 159 17 can can MD cord-326740-1fjr9qr4 159 18 occupy occupy VB cord-326740-1fjr9qr4 159 19 a a DT cord-326740-1fjr9qr4 159 20 separate separate JJ cord-326740-1fjr9qr4 159 21 payment payment NN cord-326740-1fjr9qr4 159 22 area area NN cord-326740-1fjr9qr4 159 23 in in IN cord-326740-1fjr9qr4 159 24 a a DT cord-326740-1fjr9qr4 159 25 queue queue NN cord-326740-1fjr9qr4 159 26 formed form VBN cord-326740-1fjr9qr4 159 27 in in IN cord-326740-1fjr9qr4 159 28 front front NN cord-326740-1fjr9qr4 159 29 of of IN cord-326740-1fjr9qr4 159 30 the the DT cord-326740-1fjr9qr4 159 31 cashiers cashier NNS cord-326740-1fjr9qr4 159 32 . . . cord-326740-1fjr9qr4 160 1 For for IN cord-326740-1fjr9qr4 160 2 each each DT cord-326740-1fjr9qr4 160 3 model model NN cord-326740-1fjr9qr4 160 4 , , , cord-326740-1fjr9qr4 160 5 we -PRON- PRP cord-326740-1fjr9qr4 160 6 derive derive VBP cord-326740-1fjr9qr4 160 7 and and CC cord-326740-1fjr9qr4 160 8 analyze analyze VBP cord-326740-1fjr9qr4 160 9 the the DT cord-326740-1fjr9qr4 160 10 equilibrium equilibrium NN cord-326740-1fjr9qr4 160 11 strategies strategy NNS cord-326740-1fjr9qr4 160 12 in in IN cord-326740-1fjr9qr4 160 13 terms term NNS cord-326740-1fjr9qr4 160 14 of of IN cord-326740-1fjr9qr4 160 15 the the DT cord-326740-1fjr9qr4 160 16 store store NN cord-326740-1fjr9qr4 160 17 's 's POS cord-326740-1fjr9qr4 160 18 customer customer NN cord-326740-1fjr9qr4 160 19 capacity capacity NN cord-326740-1fjr9qr4 160 20 and and CC cord-326740-1fjr9qr4 160 21 the the DT cord-326740-1fjr9qr4 160 22 number number NN cord-326740-1fjr9qr4 160 23 of of IN cord-326740-1fjr9qr4 160 24 cashiers cashier NNS cord-326740-1fjr9qr4 160 25 . . . cord-326740-1fjr9qr4 161 1 Our -PRON- PRP$ cord-326740-1fjr9qr4 161 2 findings finding NNS cord-326740-1fjr9qr4 161 3 are be VBP cord-326740-1fjr9qr4 161 4 useful useful JJ cord-326740-1fjr9qr4 161 5 and and CC cord-326740-1fjr9qr4 161 6 applicable applicable JJ cord-326740-1fjr9qr4 161 7 for for IN cord-326740-1fjr9qr4 161 8 both both DT cord-326740-1fjr9qr4 161 9 government government NN cord-326740-1fjr9qr4 161 10 authorities authority NNS cord-326740-1fjr9qr4 161 11 establishing establish VBG cord-326740-1fjr9qr4 161 12 restrictions restriction NNS