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 \\ V 
 
 REPORT NO. UIUCDCS-R72-509 
 
 COST EFFECTIVE PRIORITY ASSIGNMENT 
 IN NETWORK COMPUTERS 
 by 
 E. K. Bowdon, Sr. and W. J. Barr 
 
 March 28, 1972 
 
REPORT NO. 509 
 
 COST EFFECTIVE PRIORITY ASSIGNMENT 
 IN NETWORK COMPUTERS 
 
 *y 
 
 E. K. Bowdon, Sr . and W. J. Barr 
 
 Department of Computer Science 
 
 University of Illinois 
 
 Urbana, Illinois 
 
 (This research was supported in part by the National Science Foundation 
 under Grant No. NSF GJ 28289.) 
 
ABSTRACT 
 
 With the advent of network computers, a new area of computer systems 
 analysis has evolved. Unfortunately, most of the work which has been done 
 to date merely extends the previously existing theory of communications. While 
 this work has been very fruitful and produced important results, our analysis 
 is predicated on the assumption that a geographically distributed network 
 computer is, in reality, quite different from telephone networks and individual 
 computing centers. 
 
 In this paper, we focus our attention on the probable goals of the 
 networks and define a measure of cost effectiveness. Then using this measure 
 we develop a priority assignment technique for the individual centers that 
 comprise the network. We conclude by expanding the measure of cost effectiveness 
 to determine load leveling rules for the entire network. 
 
1. INTRODUCTION 
 
 Previously, the study of network computers has been focused on the 
 analysis of communication costs, optimal message routing, and the construction 
 of a communications network connecting geographically distributed computing 
 centers. While these problems are far from being completely solved, enough 
 progress has been made to allow the construction of reasonably efficient 
 network computers. One problem which has not been solved, however, is making 
 such networks economically viable. The solution of this problem is the object 
 of our analysis. 
 
 Our basic assumption is that economic viability for network computers 
 is predicated on efficient resource sharing. This was, in fact, a major reason 
 for the construction of several networks — to create the capability of using 
 someone else's special purpose machine or unique process without having to 
 physically transport the work. This type of resource sharing is easily 
 implemented and considerable work has been done towards this goal. There is, 
 however, another aspect of resource sharing which has not been studied thoroughly: 
 load-leveling. By load-leveling we mean the transfer of tasks between computing 
 centers for the purpose of improving the throughput of the network or other 
 criteria. We contend that the analysis and implementation of user-oriented load- 
 leveling is the key to developing economically self-supporting network computers. 
 
2. A SCENARIO OF COST EFFECTIVENESS 
 
 Until recently, efforts to measure computer efficiency have centered 
 on the measurement of resource (including processor) idle time. A major 
 problem with this philosophy is that it assumes that all tasks are of roughly 
 equal value to the user and hence the operation of the system. 
 
 As an alternative to the methods used in the past, we propose a 
 priority assignment technique designed to represent the worth of tasks in 
 the system. We present the hypothesis that tasks requiring equivalent use 
 of resources are not necessarily of equivalent worth to the user with respect 
 to time. We would allow the option for the user to specify a "deadline" 
 after which the value of his task would decrease, at a rate which he can 
 specify, to a system determined minimum. With this in mind, we propose a 
 measure of cost effectiveness with which we can evaluate the performance of 
 a network with an arbitrary number of interconnected systems, as well as 
 each system individually. 
 
 We define our measure of cost effectiveness y» as follows: 
 
 L a M-L 
 Y = (-SL) (i 3 ) 
 
 T K M ' V R-l ' 
 I 3(i) 
 i=0 
 
 where 
 
 L is the number of tasks in the queue, 
 
 q. 
 
 M is the maximum length queue, 
 
 R is the number of priority classes, 
 
 a is a measure (system-determined) of the "dedicatedness" of the 
 CPU to the processing of tasks in the queue, 
 
and 3(i) = (R-i) I (g(j)/f(j)) 
 
 J=l 
 
 where 
 
 g(j) is the reward for completing task j (a user specified 
 function of time), 
 
 and f(j) is the cost (system determined) to complete task j . 
 
 L 
 The term (rp) is a measure of the relevance of the queue to processing activities. 
 
 Similarily, we can look at B(i) as a measure of resource utilization. Note that 6(i) 
 
 indicates a ratio of reward to cost for a given priority class and is sensitive to the 
 
 needs of the user and the requirements imposed on the installation. It is 
 
 user sensitive because the user specifies the reward and is installation 
 
 sensitive because the cost for processing a task is determined by the system. 
 
 The measure of CPU dedicatedness (a), on the other hand, is an entirely 
 
 installation sensitive parameter. 
 
 The first problem which becomes apparent is that which arises if 
 
 R-l 
 I 8(i) = 0. This occurs only in the situation where there is exactly one 
 
 i=0 
 
 priority class (i.e., the non-priority case). We will finesse away this 
 
 problem by defining 
 
 M-L 
 3*-= 
 
 R-l 
 
 I 3(i) 
 i=0 
 
 for this case. Intuitively, this is obvious, since the smaller this term gets, 
 the more efficiently (in terms of reward) a system is using its resources. 
 
Furthermore, in the absence of priorities, the order in which tasks are 
 
 executed is fixed, so this term becomes irrelevant to our measure of cost 
 
 effectiveness. Thus, for the non-priority case, "we have 
 
 L a 
 Y V M ' 
 
 which is simply the measure of the relevance of the queue to processing 
 activities. This is precisely what we want if we are going to consider 
 only load-leveling in non-priority systems. However, we are interested in 
 the more general case in which we can assign priorities. 
 
 An estimate of the cost to complete task j, f(j) is readily determined 
 from the user-supplied parameters requesting resources. Frequently these 
 estimated parameters are used as upper limits in the resource allocation 
 and the operating system will not allow the program to exceed them. As a 
 result, the estimates tend to be high. On the other hand, lower priorities 
 are usually assigned to tasks requiring a large amount of resources. So 
 the net effect is, that the user's parameters reflect his best estimate and 
 we may be reasonably confident that they truly reflect his needs. 
 
 At the University of Illinois computing center, for example, as of 
 July 26, 1971 > program charges are estimated by the following formula: 
 
 cents = a(X + Y)(bZ + c) + d 
 where X = CPU time in centiseconds, 
 
 Y = number of 1/0 requests, 
 
 Z = core size in kilobytes, 
 
 a, b, c are weighting factors currently having the values 
 0.01*, 0.00^5, and 0.5, respectively, 
 
 and d is an extra charge factor including $1.00 cover charge 
 
 plus any special resources used (tape/disk storage, 
 card read, cards punched, plotter, etc.). 
 
The main significance of the reward function g(j) specified by the 
 user is that it allows us to determine a deadline or deadlines for the task. 
 Typically we might expect g(j) to be a polynomial in t, where t is the time 
 in the system. For example, the following thoughts might run through the 
 user's head: "Let's see, its 10:00 a.m. now and I don't really need immediate 
 results since I have other things to do. However, I do need the output before 
 the 3:00 p.m. meeting. Therefore, I will make 2:30 p.m. a primary deadline. 
 If it isn't done before the meeting, I can't use the results before tomorrow 
 morning, so I will make 8:00 a.m. a secondary deadline. If it isn't done by 
 then I can't use the results, so after 8:00 a.m. I don't care." 
 
 The function g(j) this user is thinking about would probably look 
 something like Figure la. Wow, this type of function poses a problem in that 
 it is difficult for the user to specify accurately and would require an 
 appreciable amount of overhead to remember and compute. Notice, however, that 
 even if turnaround time is immediate, the profit oriented installation manager 
 would put the completed task on a shelf (presumably an inexpensive storage device) 
 
 3! 30 pm 
 
 time 
 
 Cal Ideal function. 
 
 8:00 am 
 
 g(j) 
 
 9i 
 
 ft 
 
 rri2 
 
 3.30pm 8:00 am 
 
 time 
 
 (b) Approximate function. 
 
 
 Figure 1. Example of a User's Reward Function. 
 
 5 
 
and not give it to the user until just before the deadline-thus collecting 
 the maximum reward. As a result, there is little reason to specifying any- 
 thing more than the deadlines, the rewards associated with meeting the 
 deadlines, and the rate of decrease of the reward between deadlines, if any. 
 Applying this reasoning to Figure la we obtain Figure lb. Note that this 
 function is completely specified with only six parameters (deadlines t , 
 t_; rewards g , g ; and rates of decrease m , iru). 
 
 In general, we may assume that g(j) is a monotonically non-increasing, 
 piecewise linear, reward function consisting of n distinct sets of deadlines, 
 rewards, and rates of decrease. Thus we can simply specify g(j) with 3n 
 parameters. 
 
 Note that, in effect, the user specifies an abort time when the g(«j) 
 he specifies becomes less than f(j). If the installation happens to provide 
 a "lower cost" service, f(j) and if g(j) > f(j), this task would be processed, 
 but only when all the tasks with higher g(j) had been processed. 
 
 Now, what we are really interested in, is not so much an absolute 
 reward, but a ratio of reward to cost. Since f(j) is, at best, only an 
 estimate of cost, we cannot reasonably require a user to specify an absolute 
 reward. A more equitable arrangement would be to specify the rewards in terms 
 of a ratio g(j)/f(j) associated with each deadline. This ratio is more 
 indicative of the relative worth of a task, both to the system and to the 
 user, since it indicates the return on an investment. 
 
2. PRIORITY ASSIGNMENT 
 
 Let us now turn our attention to the development of a priority 
 assignment scheme which utilizes the reward/cost ratios described in the 
 previous section. We begin by quantizing the continium of reward/cost ratios 
 into R distinct intervals. Each of these intervals is then assigned to one 
 of R priority classes 0, 1, 2, ..., R-l with priority being reserved for 
 tasks with highest reward/cost ratios and priority R-l for tasks with 
 reward/cost ratios of unity or less. A task entering the system will be 
 assigned a priority according to its associated reward/cost ratio. 
 
 We want to guarantee, if possible, that all priority tasks will meet 
 
 their deadlines. Furthermore, if all priority tasks can meet their deadlines, 
 
 we want to guarantee, if possible, that all priority 1 tasks will meet their 
 
 deadlines and, in general, if all priority k tasks can meet their deadlines, 
 
 we want to guarantee that as many priority class k+1 tasks as possible will 
 
 meet their deadlines. To facilitate the priority assignment, we introduce the 
 
 following notation: 
 
 For priority k, let T. denote the i task. Then we assume for each T. 
 
 i l 
 
 that we receive the following information vector: 
 
 (T., f/g, d., t., s.) 
 
 where 
 
 T. is an identifier, 
 l 
 
 f/g is the reward/cost ratio associated with meeting the task's deadline, 
 d. is the task's deadline associated with f/g, 
 t. is the maximum processing time for the task, 
 and s. = d. - t., is the latest time at which the task may start processing 
 
 and still be assured of meeting its deadline. 
 
Now since each task has an associated deadline and maximum processing 
 time, we can use the resulting latest start time as the basis for assigning 
 positions to tasks within a priority class. A last come, first served rule 
 will be used to break ties. Additionally, we will use a compacting scheme to 
 ensure that as many tasks as possible start processing before their latest 
 start times . More formally our algorithm may be stated as follows : 
 
 Priority Assignment Algorithm 
 
 First, we assign a new task a priority based on its f/g ratio, say 
 priority k. Then within class k, its position is determined as follows: 
 
 1. Beginning with the last priority k task (that is, the task 
 
 with latest deadline) search forward until two tasks, T. ., 
 
 J-l 
 
 and T . , are found such that d. _, < d. < d.. Insert T. between the 
 J J-l i J i 
 
 two tasks, assign it a start time s. = d. - t., and renumber the 
 
 ill 
 
 tasks behind T. accordingly (i.e., T. becomes T . , T. becomes 
 J i J J 
 
 T , etc.). 
 
 2. Now, if s. n + t . .. < s. < s., n - t. there is sufficient float 
 
 J-l J-l - J - J+l J 
 
 time between T. _ and T., n for T. to be processed on time and the 
 J-l J+l J 
 
 priority assignment is complete. However, if either 
 
 s.., +T. n >s.ors. + x.>s., n ,a deadline might be missed: 
 J-l J-l J J J J+l 
 
 so we proceed with Step 3. 
 
 3 . Compacting Scheme . Let f . denote the float time between any two 
 
 J 
 
 tasks T. n and T . , where f. is defined: 
 J-l J J 
 
 f . = s. - (s. + t ) 
 J J J-l J-l 
 
 Then, F., the total float time preceding T., is given by: 
 J J 
 
 F. = I f . = s. - t + I T.. 
 J k=l J J k=l J 
 
 where t is the current time. 
 
Now, starting with task T , if s + t > s and F >_ t,, 
 
 J U J J J J 
 
 we assign a new starting time to T. given by: 
 
 J 
 
 S . = S. ... - T, . 
 J J+l j 
 
 and we continue with T. . . T. ^, etc. until we encounter a 
 
 task T, , k ^ j , such that s. < s. . - T. . (Note that T. . 
 k k — k+1 k j+l 
 
 and all its predecessors are guaranteed to meet their deadlines.) 
 
 h. However, if s. + x. > s... but F. < t., we do not assign a new 
 J J J+l J J 
 
 start time to T . . Instead we leave the start time at its latest 
 J 
 
 critical value, even though it may not start processing at that 
 
 time. We observe that many tasks may not require all of the 
 
 processing time specified by their maxima, and as a result 
 
 sufficient float time may be created later to enable the task, 
 
 T., to meet its deadline. 
 J 
 
 Examples . 
 
 Several examples will now be given to illustrate the efficacy of the 
 algorithm. Suppose we have determined that a task, T. , should have priority k 
 and that at time t = 0, the state of priority class k is that shown in Figure 2. 
 (Note that since all priority class k tasks have similar f/g, we need not show 
 these ratios.) Notice that forming the float time column is analogous to forming 
 a forward difference table. In each of the following examples we assume that 
 Figure 2 is the initial state of priority class k. 
 
 i) Suppose the information vector (with f/g omitted) for T. is (T. ,6,1,5) 
 Beginning with T , we observe that d < d. <_ d < d, < d . So we 
 insert T. between T and T and renumber the tasks accordingly. 
 
I I I I I I 
 
 0123456789012345 
 
 Ti 
 
 T 2 
 
 T 4 T 5 
 
 a) schedule of tasks, 
 
 Tx 
 
 d! = 2 
 Ti - 1 
 Si = l 
 
 T 2 
 
 d 2 = 4 
 T 2 = 2 
 S 2 = 2 
 
 T 3 
 
 d 3 = 10 
 T 3 = 3 
 S3 = ^ 
 
 T 4 
 
 d 4 = 14 
 T 4 = 2 
 S 4 = 12 
 
 T 5 
 
 d 5 = 15 
 S 5 = 14 
 
 v_ 
 
 J 
 
 INFORMATION VECTOR FLOAT TIME; f i 
 
 B) INFORMATION VECTORS. 
 
 FIGURE 2 -STATE OF PRIORITY CLASS K AT TIME t = 
 
 10 
 
Now s n + T- < s_ < s, - t_ since 2 + 2 < 5 < 7 - 1, so the priority 
 2 2—0—4 5 — — 
 
 assignment is complete and all tasks are guaranteed to meet their 
 
 deadlines. The resulting state of priority class k is shown in 
 
 Figure 3. 
 
 ii) Suppose instead that the information vector for T. is (T. ,9,2,7). 
 
 We find that &_ < d, < d_ < d, < d.., so we insert T. between T 
 21—34 5' i 2 
 
 and T and renumber the tasks accordingly. However, s + x > s, 
 
 since 7 + 2 > 7 and a deadline could he missed. But F >_ x since 
 
 h >_ 3, so we assign a new start time to T : s = s, - x = 7 - 2 = 5. 
 
 Now s < s - x since 2 <_ 5 - 2, so the priority assignment is 
 
 complete and all tasks are guaranteed to meet their deadlines. The 
 
 resulting state of priority class k is shown in Figure k. (Note 
 
 the effect of the last in first out rule for breaking ties on 
 
 start times. ) 
 
 iii) Next suppose the information vector for T. is (T.,9,^,5). We find 
 
 that d_. < d. < d„ < d, < d_, so we insert T. between T^ and T„ 
 2 i — 3^5 i 23 
 
 and renumber the tasks accordingly. However, s„ + x > s« since 
 5 + h > 7» and a deadline could be missed. But F >_ x since k >_ k, 
 so we assign a new start time to T : s^ = s. - x_ = 7 - h = 3. 
 Next s + x > s since 2 + 2 > 3, so we assign a new start time 
 to T : s = s - x = 3 - 2 = 1. Now s + x > s since 1 + 1 > 1, 
 so we assign a new start time to T : s = s - x = 0. The priority 
 assignment is complete and all tasks are guaranteed to meet their 
 deadlines. The resulting state of priority class k is shown in 
 Figure 5- 
 
 11 
 
I I I I I I 
 
 0123456789012345 
 
 Ti 
 
 T 2 
 
 T, 
 
 T 4 T 5 
 
 a) schedule of tasks before assignment. 
 
 3 4 5 6 
 
 8 9 
 
 I 
 
 
 
 I 
 
 2 
 
 I I I 
 
 3 4 5 
 
 T x 
 
 T 2 
 
 T: 
 
 T, 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment, 
 
 
 
 t 
 
 Tx 
 
 
 2 
 1 
 1 
 
 T 2 
 
 
 4 
 2 
 2 
 
 \ 
 
 T 3 
 
 6 
 
 1 
 5 
 
 ^ 
 
 T 4 
 
 10 
 3 
 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 12 
 
 % 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 c) information vectors after assignment. 
 
 FIG. 3- RESULTS OF PRIORITY ASSIGNMENTS 
 FOR EXAMPLE ( j ) 
 
 12 
 
I I I I I I 
 
 0123456789012345 
 
 \ 
 
 T 2 
 
 T 3 
 
 
 Ta 
 
 T 5 
 
 
 
 
 
 T| 
 
 
 a) schedule of tasks before assignment, 
 
 234567890 
 
 I I I I 
 
 2 3 4 5 
 
 Ta 
 
 T 2 
 
 T 3 
 
 T 4 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment. 
 
 
 
 t 
 
 T, 
 
 
 2 
 
 1 
 1 
 
 T 2 
 
 
 4 
 2 
 2 
 
 X 
 
 T 3 
 
 9 
 2 
 5 
 
 \ 
 
 T 4 
 
 10 
 3 
 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 
 12 
 
 \ 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 c) information vectors after assignment, 
 
 FIG, 4 -RESULTS OF PRIORITY ASSIGNMENTS 
 FOR EXAMPLE ( i i ) 
 
 13 
 
I I I I I I 
 
 0123456789012345 
 
 Ti 
 
 T 2 
 
 
 T 3 
 
 
 T 4 
 
 T 5 
 
 
 
 
 
 
 
 
 
 
 
 
 T, 
 
 
 
 a) schedule of tasks before assignment. 
 
 I I I I I I 
 
 23456789012345 
 
 Ti 
 
 T 2 
 
 T 3 
 
 T 4 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment. 
 
 T x 
 
 
 2 
 
 1 
 
 
 T 2 
 
 
 4 
 2 
 
 1 
 
 H 
 
 T 3 
 
 9 
 4 
 3 
 
 ^ 
 
 T 4 
 
 10 
 3 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 12 
 
 % 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 c) information vectors after assignment. 
 
 FIG. 5 -RESULTS OF PRIORITY ASSIGNMENTS 
 FOR EXAMPLE ( i i i ) 
 Ik 
 
iv) As a final example, suppose that the information vector for T. 
 is (T.,9,5,U). As before, we find that d < d. <_ d < d, < d , 
 so we insert T. between T^ and T and renumber the tasks accordingly. 
 However, s_ + t > s. since k + 5 > 7, and a deadline could be 
 missed. Furthermore, F < x_ since h < 5, and the compacting scheme 
 will not help us. Instead we leave the start times at their latest 
 critical values and hope that sufficient float time is created 
 later to enable the tasks to meet their deadlines. The results 
 of this assignment are shown in Figure 6. Note that T is the 
 task which is in danger of missing its deadline. 
 The last example brings up the problem of what to do with a task whose 
 deadline is missed. We simply treat it as though it had just entered the 
 system using the next specified deadline as the current deadline. If no 
 further deadlines are specified, the task is assigned priority R-l and will be 
 processed accordingly. 
 
 When a processor finishes executing a task the following scheduling 
 algorithm is used to determine which task is to be processed next. Generally, 
 the algorithm takes the highest priority task in the queue that Is closest to 
 its latest starting time. 
 
 Scheduling Algorithm 
 
 Beginning with k=0. 
 
 1. We examine the float time, f , for the first task in priority class k. 
 Then for I = k+1: 
 
 15 
 
I I I I I I 
 
 0123456789012345 
 
 Ti 
 
 T 2 
 
 
 T 3 
 
 
 T 4 
 
 T 5 
 
 
 
 
 
 
 
 
 
 
 
 
 Ti 
 
 
 
 a) schedule of tasks before assignment. 
 
 234567890 
 
 I I I I 
 
 2 3 4 5 
 
 Ti 
 
 T 2 
 
 T. 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment. 
 
 
 
 t 
 
 Tx 
 
 
 2 
 
 1 
 1 
 
 T 2 
 
 
 4 
 2 
 2 
 
 X 
 
 T 3 
 
 9 
 4 
 5 
 
 \ 
 
 1 4 
 
 r 10 
 3 
 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 12 
 
 \ 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 C) INFORMATION VECTORS AFTER ASSIGNMENT. 
 
 FIG. 6- RESULTS OF PRIORITY ASSIGNMENTS 
 FOR EXAMPLE ( i V ) 
 
 16 
 
2. If f of priority class k <_t for the first task of priority- 
 class &, we set k.=l and continue with Step 1. Otherwise we 
 continue with Step 3. 
 
 3. Set H = 2.+1 and continue with Step 2 until all priority classes 
 have been considered. Then continue with Step k. 
 
 h. Assign the first task, T , in priority k to the available processor. 
 
 In the foregoing we have tacitly assumed that each task enters the 
 system sufficiently before its deadline to allow processing. The two algorithms 
 taken together facilitate meeting the deadlines, where possible, of the higher 
 priority tasks. Those tasks which do not meet their deadlines will tend to be 
 uniformly late. 
 
 IT 
 
3. LOAD LEVELING IN A NETWORK OF CENTERS 
 
 Thus far we have been concerned only with cost effectiveness in a 
 single center. Next, let us consider the more general problem of load 
 leveling within a network of centers. Each center may contain a single computer 
 or a subnet of computers. The topological and physical properties of such networks 
 have been illustrated (1,5,6,7) and will not be discussed here. 
 
 We wish to determine a strategy which optimizes the value of work 
 performed by the network computer. That is, to guarantee that every task in 
 each center will be processed, if possible, before its deadline and only those 
 tasks that offer the least reward to the network will miss their deadlines. Implicit 
 in this discussion is the simplifying assumption that any task can be performed 
 in any center. Removal of this restrictive assumption leads to many interesting 
 problems for future research. 
 
 We define the measure of cost effectiveness for a network of N centers, 
 
 y, T , as follows : 
 
 N N 
 
 y, t = T w.y. given that V u>. = 1 
 'N . L . i' 1 . L . i 
 
 i=l i=l 
 
 where 
 
 the to. are weighting factors that reflect the relative contribution of 
 
 the i center to the overall computational capability of the network, 
 
 th 
 and y. is the measure of cost effectiveness for the i center. 
 i 
 
 Note that if a center is a subnet of computers, we could employ this definition 
 to determine the measure of cost effectiveness for the subnet. We also let c. . 
 denote the cost of communication between centers i and j; and t as the transmissior 
 time between centers i and j . 
 
 18 
 
Ideally, we want the network computer to operate so that all tasks within 
 the network are processed before their deadlines. If a task is in danger of 
 missing its deadline, we want to consider it as a candidate for transmission to 
 another center for processing. The determination of which tasks should be transferred 
 follows the priority assignment (i.e., priority tasks in danger of missing 
 deadlines should be the first to be considered, priority 1 tasks next, etc.). 
 
 We note that this scheme may not discover all tasks that are in danger 
 of missing their deadlines. In order to discover all tasks that might be in danger 
 of missing their deadlines, we would require a look ahead scheme to determine the 
 available float time and to fit lower priority tasks into this float time. The value 
 of such a scheme is questionable, however, since we assume some float time is 
 created during processing and additional float time may be created by sending 
 high priority tasks to other centers. Also, the overhead associated with 
 executing the look ahead scheme would further reduce the probable gain of 
 such a scheme. 
 
 The determination of which center should be the recipient of a 
 transmitted task can be determined from the measure of cost effectiveness of 
 each center. Recall that the measure indicates the worth of the work to be 
 processed within a center. Thus, a center with a task in danger of missing 
 its deadline will have a larger measure than a center with available float 
 time. Thus, by examining the measures for each center, we can determine the 
 likely recipient of tasks to be transmitted. These centers can in turn, 
 examine their own queues and bid for additional work on the basis of their 
 available float time. This approach has a decided economic advantage over broad- 
 casting the availability of work throughout the network and transmitting the tasks 
 to the first center to respond (h) . 
 
 19 
 
Once a recipient center has been determined, we would transmit a 
 given task only if the loss in reward associated with not meeting its deadline 
 is greater than c.., the cost of transmitting the task between centers and 
 transmitting back the results. 
 
 When a task is transmitted to a new center its deadline is diminished 
 by t. ., the time to transmit back the results, thus ensuring the task will 
 
 J- J 
 
 reach its destination before its true deadline. Similarly, the reward 
 associated with meeting the task's deadline is diminished by c.., since this 
 represents a reduction in profit. Then the task's f/g ratio is used to 
 determine a new priority and the task is treated like one originating in 
 that center . 
 
 This huristic algorithm provides the desired results that within each 
 center all deadlines are met, if possible, and if any task is in danger of 
 missing its deadline, it is considered for possible transmission to another 
 center which can meet the deadline. 
 
 20 
 
h . SUMMARY 
 
 We have introduced a priority assignment technique which, together 
 with the scheduling algorithm, provides a new approach to resource 
 allocation. The most important innovation in this approach is that it allows 
 a computing installation to maximize reward for the use of resources while 
 allowing the user to specify deadlines for his results. The demand by users 
 upon the resources of a computing installation is translated into rewards for 
 the center. 
 
 This approach offers advantages to the user and to the computing 
 installation. The user can exercise control over the processing of his task 
 by specifying its reward/cost ratio which, in turn, determines the importance 
 the installation attaches to his requests. The increased flexibility to the 
 user in specifying rewards for meeting deadlines yields increased reward to 
 the center. Thus the computing installation becomes cost effective, since for 
 a given interval of time, the installation can process those tasks which return 
 the maximum reward. A notable point here, is that this system readily lends 
 itself to measurement. 
 
 The measure of cost effectiveness is designed to reflect the status of 
 a center using the priority assignment technique. From its definition, the 
 value of the measure depends not only on the presence of tasks in the system 
 but upon the priority of these tasks. Thus the measure reflects the worth of 
 the tasks awaiting execution rather than just the number of tasks. Therefore, 
 the measure can be used both, statically, to record the operation of a center 
 and, dynamically, to determine the probability of available float time. This 
 attribute enables us to predict the worth of the work to be performed in any 
 center in the network and facilitates load-leveling between centers. 
 
 21 
 
Finally, our approach treats a network computer as the economic entity 
 that it should be: a market place in which vendors compete for customers and 
 in which users contend for scarce resources. The development of this approach 
 is a first step in the long road to achieving economic viability in network 
 computers. 
 
 22 
 
REFERENCES 
 
 1. Abramson, Norman, The AL0HA System , University of Hawaii Technical Report, 
 January, 1972. 
 
 2. Bowdon, E. K., Sr . , "Dispatching in Network Computers," Proceedings of 
 the Symposium on Computer-Communications , Networks and Teletraf fie , 
 April, 1972. 
 
 3. Bowdon, E. K., Sr . , and W. J. Barr, "Throughput Optimization in Network 
 Computers," Proceedings of the Fifth International Conference of Systems 
 Sciences , Honolulu, January, 1972. 
 
 k. Farber, David J., and Kenneth C. Larson, Supplement to Proposal for 
 Research Submitted to the National Science Foundation on Distributed 
 Computing System , University of California at Irvine, Technical Report, 
 October, 1970. 
 
 5. Frank, H., and I. T. Frisch, Communication , Transmission and Transportation 
 Networks , Addi son-Wesley, 1971. 
 
 6. Kleinrock, L., Communication Nets ; Stochastic Flow and Delay , McGraw-Hill, 
 New York, 196k. 
 
 7. Syski, R. , Introduction to Congestion Theory in Telephone Systems , Oliver 
 and Boyd, Edinburgh, i960. 
 
 23 
 
IBLIOGRAPHIC DATA 
 HEET 
 
 1. Report No. 
 
 UIUCDCS-R72-50Q 
 
 "Title .in.i Subt itlr 
 
 Cost Effective Priority Assignment in Network Computers 
 
 3. Recipient's Accession No. 
 
 5- Report Date 
 
 March 1972 
 
 \utliori* ■* 
 
 Edward K. Bowdon, Sr. and William J. Barr 
 
 8. Performing Organization Rept. 
 No. 
 
 Performing Organization Name and Address 
 
 Department of Computer Science 
 University of Illinois 
 Urbana, Illinois 6l801 
 
 10. Project/Task/Work Unit No. 
 
 11. Contract/Grant No. 
 
 NSF GJ 28289 
 
 I Sponsoring Organization Name and Address 
 
 National Science Foundation 
 Washington, DC 
 
 13. Type of Report & Period 
 Covered 
 
 Research 
 
 14. 
 
 5. Supplementary Notes 
 
 ;. Abstracts 
 
 With the advent of network computers, a new area of computer systems analysis 
 as evolved. Unfortunately, most of the work which has been done to date merely 
 xtends the previously existing theory of communications. While this work has been 
 ery fruitful and produced important results, our analysis is predicated on the 
 sumption that a geographically distributed network computer is, in reality, quite 
 ifferent from telephone networks and individual computing centers. 
 
 In this paper, we focus our attention on the probable goals of the networks 
 define a measure of cost effectiveness. Then using this measure we develop a 
 iority assignment technique for the individual centers that comprise the network, 
 conclude by expanding the measure of cost effectiveness to determine load leveling 
 ules for the entire network. 
 
 '. Key Words and Document Analysis. 17a. Descriptors 
 
 Network Computer, Queueing Theory, System Modeling, Throughput Analysis 
 Dispatching, Load Leveling 
 
 b. Identifiers/Open-Ended Terms 
 
 c COSATI Field/Group 
 
 •Availability Statement 
 
 Release unlimited 
 
 R M NTIS-35 
 
 19. Security Class (This 
 Report) 
 
 UNCLASSIFIED 
 
 20. Security Class (Ihis 
 Page 
 
 UNCLASSIFIED 
 
 21. No. of Pages 
 
 23 
 
 22. Price 
 
 USCOMM-DC 40329-P7I 
 
1 V