College and Research Libraries JOHN J. REGAZZI and RODNEY M. HERSBERGER Queues and Reference Service: Some Implications for Staffing In most organizations activities occur that produce waiting lines or queues. This study, undertaken at a medium-sized academic library, attempts through the use of a simulation technique ( 1) to analyze the extent to which queues develop at a reference desk during peak periods, (2) to propose al- ternative staffing models to reduce queues, and (3) through the use of a cost- effectiveness formula to examine the merits of the proposed alternatives. THIS PAPER IS a case history of some staffing and service patterns at the reference desk of a medium-sized academic library. The study, however, is also an effort to apply standard quantitative techniques, i.e . , queuing models and simulation, to a library management problem in the area of public services. These techniques, developed in business, industry, and science, have been widely used in such library areas as circula- tion, 1 library administration, 2 and technical services. 3 This particular case attempts to evaluate or "measure" reference services beyond the compilation of "reference statis- tics" that emphasize the evaluation of past performance or defend the value of a refer- ence service. 4 The emphasis here is on present services and staffing requirements for optimizing that service within the budgetary constraints of a particular library. In 1974 in a "Sym- posium on Measurement of Reference," it was stated that "the number one need for statistical information centered on informa- tion for staffing patterns including peak and idle periods, subject specialization and non-desk time."5 Using certain quantitative techniques, this study illustrates how . john ]. Regazzi is director of documentation seroices, The Foundation Center, New York, and a doctoral student at Rutgers University . Rodney M. Hersberger is assistant to the library director, Northern Illinois University, DeKalb. various alternative staffing patterns for peak period services can be compared and eval- uated. DEFINITIONS As in many service organizations, there exist processes that produce waiting lines or queues. In the operation of an information desk, a queue is defined as occurring when a patron or employee must wait because the desk, operating at capacity, is temporarily unable to provide service. A second term used in this study is "model." Although there are various types of models, for the purpose of this study the tenn model refers to the symbolic repre- sentation in tabular form of the reference service. Although four models were de- veloped in the study, only one is shown here as an example of the management technique known as a "simulation." The data necessary to develop a simulation model were obtained by sampling patron arrival time and service time during peak periods for several weeks. PURPOSE This study, conducted in the library at Northern Illinois University, DeKalb, was initially undertaken because of the authors' observations of long waiting times for refer- ence service during peak periods and be- cause of staff observations relative to in- creased service demands during these same I 293 294 I College & Research Libraries • july 1978 periods. At the time of the study, there were approximately 18,000 students (FfE) at the university, and reference service in the university library was provided through a general reference desk on the library's main floor. Although the reference department had kept certain statistics, these data were not helpful in dealing with waiting lines. The study, then, had two purposes: (1) to evalu- ate the extent to which queues develop at an information desk and (2) through the use of simulation models and cost analyses to develop alternative staffing patterns which might increase the effectiveness of the service. METHODOLOGY For approximately one year prior to this study, the reference department kept statis- tics on an hourly basis for the following categories: (1) the number of persons using the reference room, (2) the number of directional questions answered by the de- partment, and (3) the number of "reference" or research questions answered by the de- partment. In order to develop a queuing model, the arrival time intervals of users at the reference desk and the service times of staff for the various types of questions an- swered were needed as well. The library was utilizing a single- channel/single-stage reference station, and thus the reference desk was always staffed by one professional librarian, but very rarely by more than one. It was decided to confine the study to the library's most heav- ily used periods only. Obviously, the queues would be most severe during these times with any acceptable alternatives appli- cable to other times of the day if so desired. Through a review of the statistics already gathered by the reference department, the peak periods were established. The arrival times of patrons and the service times of staff during these periods were randomly · sampled over a period of six months. Because of the demand on the reference department during peak periods, many li- brarians felt that s~rvice was necessarily "shortened," i.e., less time was spent with each patron because of the heavy number of requests during these periods. It was also decided to obtain service times for nonpeak periods. These observations were also ran- domly sampled over a period of six months. As one might expect, the increased service time does not occur in the directional ques- tions, most of which can be answered in .5-1.0 minutes, but rather in the longer research-oriented questions. PRESENT MODEL A representation of the present operating reference service was then developed (see table 1). This model used the arrival times and service times for peak periods. Since neither arrival times nor service times are constant or uniform, a random number se- quence was used in selecting each. Thus RN represents the random number se- quence for the arrival times, and RN 1 the sequence for service times. In each case the two-digit number is matched with a ranking sequence for arrival intervals and service times which were obtained in the sampling period. For example, for the first arrival the random number selected was 52, which cor- responds to an arrival interval value of 1. 5 minutes. Thus our first patron arrived at 1 minute and 30 seconds after the start of the simulation. Similarly, a random number was selected for this patron's service time; the RN 1 of 26 corresponds to a service time of .5 minutes; therefore, the first patron arriv- ing :01:30 after the hour experienced no de- lay, and the service was completed in 30 seconds at :02:00. The librarian, however, in this instance experienced an idle time of 1.5 minutes in waiting for the patron to arrive. The model was thus developed for 30 minutes of arrivals, with some large queues occurring in the process. It should be noted that some twenty'"five patrons in approxi- mately a half-hour period would experience a total delay time of 146.5 minutes during peak periods, while the librarian experi- ences a total of 3 minutes idle time. The average delay time per patron is 5.86 min- utes, with individual delays of up to 12.25 minutes. During the sampling, it was our observation that queues of this magnitude did occur occasionally; however, in certain instances individuals would leave the queue. One of the most serious weaknesses of this one-channel system is for the indi- vidual who has a relatively simple direc- I I ~ Queues and Reference Service I 295 TABLE 1 SIMULATION OF PRESENT SERVICE DURJNG PEAK HOURS CUM Arrival Arrival Delay Arrival RN Interval Time Time 1 52 1.5 01:30 2 75 2.0 03:30 3 49 1.0 04:30 4 05 0.0 04:30 1.0 5 21 0.25 04:45 9.25 6 18 0.25 05:00 10.5 7 55 1.5 06:30 11.0 8 13 0.25 06:45 12.25 9 51 1.5 08:15 10.25 10 99 5.5 13:45 5.75 11 02 0.0 13:45 6.25 12 43 1.0 14:45 5.75 13 42 1.0 15:45 5.25 14 47 1.0 16:45 3.25 15 77 2.5 19:15 3.75 16 03 0.0 19:15 6.75 17 13 0.25 19:30 7.0 18 63 1.5 21:00 8.0 19 44 1.0 22:00 7.5 20 60 1.5 23:30 7.5 21 05 0.0 23:30 8.0 22 83 3.0 26:30 5.5 23 38 1.0 27:30 5.0 24 67 2.0 29:30 4.0 25 39 1.0 30:30 3.5 tional question-which might take only .5 to 1. 0 minutes to answer-but who must wait as long as 5 to 12.25 minutes. Using the same single-channel/single- stage service model and the same arrival patterns, a simulation was done substituting nonpeak period service times for the peak period times. As expected, the queues were substantially longer for the same time pe- riod, and the same number of patrons would experience a projected total delay time of 202.5 minutes, with 8.1 minutes of delay time per patron. Thus, according to this simulation the present reference service represents a "shortened" service by 27.6 percent during peak periods compared to non-peak period services. These delay times represent the worst possible cases, where no patrons leave the queue. Another simulation would include an estimate of the number of patrons who temporarily drop out of the queue and re- turn later; however, such data were not col- lected and are not available here. Regard- less of whether t4e patron remained in the queue or not, the reference desk was operating at capacity and was, therefore, Service Idle RNl Time Start Finish Time 26 0.5 01:03 02:00 1.5 63 . 1.0 03:30 04:30 1.5 51 1.0 04:30 05:30 99 9.0 05:30 14:30 64 1.0 14:30 15:30 75 2.0 15:30 17:30 35 0.5 17:30 18:00 07 0.5 18:00 18:30 42 1.0 18:30 19:30 10 0.5 19:30 20:00 04 0.5 20:00 20:30 35 0.5 20:30 21:30 13 0.5 21:30 22:00 63 1.0 22:00 23:00 87 3.0 23:00 26:00 81 2.5 26:00 28:30 31 0.5 28:30 29:00 05 0.5 29:00 29:30 48 1.0 29:30 30:30 49 1.0 30:30 31:30 04 0.5 31:30 32:00 28 0.5 32:00 32:30 48 1.0 32:30 33:30 22 0.5 33:30 34:00 67 1.5 34:00 35:30 temporarily unable to provide service to that patron. ALTERNATIVE MODELS Given the amount of reduction in the peak-period reference service that had al- ready occurred, it was obvious that pro- cedural changes attempting to further shorten the service seemed to be futile for two reasons. First, the demand for refer- ence service during these periods is so great that even if the reference process could be further shortened, it would not substantially reduce the queue. Second, any further re- duction of service might seriously com- promise the quality of the service during this time. Therefore, some expansion of staff was necessary, and various alternatives were analyzed. The alternative staffing patterns attempt to utilize both professional and nonprofes- sional personnel. There is substantial evi- dence for using nonprofessional personnel to staff a reference desk. Dawson has re- marked "in reference work there is much that can be done by nonprofessionals under supervision. They can answer many direc- 296 I College & Research Libraries • july 1978 tional and informational questions, freeing the professional for the more difficult and extensive 'research' question."8 Rogers and Weber agree that nonprofessionals can handle many of the directional and interpre- tive questions asked at reference desks in college libraries. 7 Bloomberg holds a similar view that allowing a nonprofessional to be the patron's first contact will free a librarian from the time-consuming task of answering directional and ready reference questions. 8 In their survey of colleges and smaller universities with enrollments up to 6,000 students, Boyer and Theimer found that in "69 percent of the reporting libraries, non- professionals are used at the reference desk. "9 Of the three alternative models dis- cussed below, two models add nonprofes- sional staff only, and the third uses a full- time professional librarian. One proposed alternative, a two-stage, single-service facility, would consist of a student and a librarian working together during busy periods. The student would be trained to conduct the initial reference interview and determine if the question would need to be answered by the librarian. If so, the patron would be referred to the librarian. In order to simulate this proce- dure, an estimation was needed of what portion of the service could be handled by the student. Again, by using the statistics compiled by the reference department prior to this study, it was determined that most direc- tional questions required .5 to 1.0 minutes. It was estimated that the student would be able to answer 80 percent of the .5-minute questions and 50 percent of the 1.0-minute questions. These estimations were arrived at through discussions with the reference staff and an analysis of the various subcategories of directional questions. Under this multistage, single-channel ap- proach, the user experiences a substantially reduced amount of delay time-in fact, only a total of 20.75 minutes or an average of .83 minutes per patron. Moreover, only one pa- tron experienced a delay of over 3 minutes. The librarian has an increased idle time of 7. 75 minutes, and the student's idle time is 21.75 minutes. Although a more complete cost analysis will be discussed in the next section, it may be noted that since student workers are hired at mmtmum wages and on a per diem basis, this model will only in- crease the cost of reference service about $.05 per patron during peak periods. Next, a simulation was developed using the same multistage service channel for peak periods but substituting nonpeak ser- vice times. The patron under these condi- tions experienced a total of 49.25 minutes delay time or an average of 1. 97 minutes per patron. Two patrons, however, would experience delays of over 10 minutes, but the remainder were substantially lower. Idle time for the librarian is somewhat less than under the present service conditions (i.e. , 3. 75 minutes), and the student idle time of 20.25 minutes is approximately the same for both models. Three other alternative simulation models were considered. One model would place a professional librarian at stage one of a two- stage service channel with a student assis- tant at stage two. This model has the disad- vantage of requiring the librarian to field all questions and then referring the patron to a student who could answer some of the directionalllocational questions. This idea was dismissed as being even more impracti- cal than the current system. A second model would place two profes- sional librarians, in parallel, at a service point to simulate two single-stage service channels. This model would indeed afford users better service: total delay time for twenty-five arrivals was only 1.5 minutes. Librarian idle time, however, increased to 42.5 minutes. The increased effectiveness, however, must be examined in relationship to the corresponding increase in costs. This proposal will be discussed further in the next section. The final model, a further variation of the previous models, involves the simulation of two single-stage channels, i.e., a librarian and a student in parallel rather than in tan- dem. Through observation and further dis- cussion with reference department person- nel, it was determined that 60 percent of the users arriving at this information center would first approach the librarian. As in ear- lier simulations, it · was estimated that the student would. be able to answer 80 percent of the .5-minute questions and 50 percent of the 1.0-minute questions. It was assumed, of course, that if one of the two staff mem- bers were engaged, the users would ap- proach the other. If the student was unable to answer a question, the patron would then be referred to the professional. · This simulation produced a total delay time of 71.25 minutes, or an average of 2.85 minutes per patron. Eleven patrons, how- ever, encountered no delay at all. The de- lays, then, were caused by several longer reference questions coming in succession. Idle time in this model was 27 minutes, with the student assistant experiencing 22.5 minutes of that idle time and the librarian 4.5 minutes. The librarian was obviously busy during the simulated period, but that staff member's efforts were primarily di- rected to longer reference questions, rather than directional questions. In summing up these models, they range from the present service on one end to the two-librarian model on the other end. The first model is obviously the least costly, yet incapable of any expansion, while the last model, which is very efficient for the pa- trons' time, is extremely costly to the li- brary. The next section attempts to compare these models using a common denomination of cost effectiveness. COST ANALYSIS As a basis for quantitative analysis, a common means of comparing the four models was developed. Obviously none of the individual factors-costs (c), idle time (i), or delay time (d)-would suffice alone, since the selected measure must incorporate each of the factors. A simple cost- effectiveness formula was developed with the effectiveness measure (r) derived as fol- lows: 1 r = d + i c The formula has two conditions that may not be obvious but that must be mentioned here. First, the formula assumes that delay time for patrons and idle time for staff are of equal weight to the library. In other words, it is as important not have patrons waiting as it is not to have staff idle. Second, the formula cannot derive r in all circumstances; r is indeterminable when both i = 0 and Queues and Reference Service I 297 d = 0. It may be argued, however, that this is the ideal situation, since every patron is completely serviced without delay and no staff member is ever idle. A summary table was compiled, which in- cludes the total idle time, total delay time, and total costs for each model (see table 2). The costs and idle times were divided, when appropriate, between professionals and students. In order to make the formula sensitive to the different costs and idle times for librarians and students, it needed to be revised for the student/professional model: 1 1 cl c2 where i 1 represents the idle time for pro- fessionals; i 2 represents the idle time for stu- dents; c 1 represents professional costs; c2 r~presents student costs. Finally, since it is immaterial for measur- ing the cost effectiveness of a system whether the patron is awaiting service from a student or a professional, the total delay time is arbitrarily divided across both of the effectiveness measures. Substituting the values in table 2, the following effectiveness measures are derived: Model 1. Present Effectiveness Rating r = .0007 2. Student/Professional (in tandem) 3. Professional/Profes- sional (in parallel) 4. Student/Professional (in parallel) r = .0159 r = .0082 r = .0090 Although the simulated model of the pre- sent reference service is the least costly to the library, it is also by far the least effec- tive, as measured by the cost-effectiveness formula above, of any of the models pre- sented. Because of the model's low effec- tiveness rating, some change would seem appropriate. Because of its high cost, the professional/professional model could not be seriously considered vis-a-vis either of the 298 I College & Research Libraries • July 1978 TABLE 2 SUMMARY TABLE FOR DELAY TIMES, IDLE TIMES AND COSTS. Total Delay Student Professional Student Professional Model Time Idle Time Idle Time Costs Costs (Dollars (Dollars per hour)* per hour)* 1. Present Model 146.5 3 $10 2. Student/Pro- fessional Model. 20.75 21.75 7.75 $3 $10 3. ProfessionaV Professional 1.5 42.5 $20 Model 4. Student/Pro- fessional (in 71.25 22.5 4.5 $3 $10 parallel) '"'The costs represent approximate average hourly costs for professional and student employees at the time of the study. student/professional models. Of these two remaining models, the student/professional model working in paral- lel causes the patron much more simulated waiting time. Thus the single-channel, two- stage service provides the highest cost- effectiveness rating. Since a student could be employed part time during the peak pe- riods, this model would significantly de- crease waiting lines, while only modestly increasing reference service costs. IMPLEMENTATION The library that was studied here moved to a new building between the time the data were gathered and first analyzed and the date of publication. Reference services changed from a highly centralized operation to a very decentralized arrangement. In fact, the library changed to a subject divi- sion arrangement, including reference ser- vices. There are now ten reference points. Because of the move, direct implementa- tion of any of the models was not possible. The library, however, does utilize a varia- tion of the student/professional model and another approach as well. In theory, one professional librarian is always on duty on each floor. A graduate assistant is stationed in each reference area in the evenings when the librarian is not on duty. These graduate assistants answer those questions that they can and refer the others to the librarian on . duty on the floor. During the day a library clerk is on duty on each floor to help direct and refer patrons and to answer the tele- phone and make the necessary referrals. The first contact with a patron is made by a · nonprofessional employee, and the princi- ples of a multistage, single-channel refer- ence· service have been employed in this reference department. REFERENCES 1. W. M. Shaw, Jr., "Computer Simulation of the Circulation System of a Library," Journal of the American Society for InfonnatiQn Sci- ence 25:271-79 (1975). 2. Irving E. Stephens, "Computer Simulation of Library Operations: An Evaluation of an Ad- ministrative Tool," Special Libraries 61:280-83 (July/Aug. 1970). 3. Phyllis A. Richmond, "Classification from PRECIS: Some Possibilities," Journal of the American Society for Information Science 27:240-47 (1976). 4. Manual D. Lopez, "Academic Reference Ser- vice: Measurement, Costs and Value," RQ 12:234--42 (Spring 1973). 5. "Symposium on Measurement of Reference," RQ, 14:8 (Fall1974). 6. John M. Dawson, "Not Too Academic," Col- lege & Research Libraries 27:39 Qan. 1966). 7. Rutherford Rogers and David C. Weber, Uni- versity Library Administration (New York : Wilson, 1971), p.210. 8. Marty Bloomberg, Introduction to Public Services for Library Technicians (Littleton, Colo.: Libraries Unlimited, 1977), p.86. 9. Laura M. Boyer and William C. Theimer, Jr., "The Use and Training of Non professional Personnel at Reference Desks in Selected Col- lege and University Libraries," College & Re- search Libraries 36:195 (May 1975).