College and Research Libraries WILLIAM B. ROUSE and SANDRA H. ROUSE Use of a Librarian[Consultant Team To Study Library Operations A team approach to analysis of library operations is suggested. A spe- cific example of staffing library information desks illustrates the com- plementary characteristics and advantages of using a librarian/ con- sultant team. The example shows how lines of thought are developed by the team and the important aspects of cooperation between team members. !NTRODUCI'ION THE IDEA OF APPLYING SYSTEMS-ANAL- YSIS TECHNIQUES to study library opera- tions is becoming quite popular.! As com- plexity of the system increases, it certain- ly seems that logical analysis is necessary if the efficiency of a library system is to be maintained. However, several difficul- ties arise. The most obvious problem is that li- brarians usually have, at most, only a cursory knowledge of the analytical tools available. The solution might be for the library to employ a full-time analyst on its staff. 2 However, budgets and needs may limit this solution. Librarians might be trained to use various "canned" models of library op- erations. If such quasi-analysts, how- ever, do not understand the theoretical base of such models, they will have dif- ficulty modifying the models for a par- ticular library system, as well as keeping up with developments in mathematical modeling. Mr. Rouse is research associate, Depart- ment of Mechanical Engineering, Massa- chusetts Institute of Technology, Cam- bridge, Massachusetts; Ms. Rouse is senior library assistant, Science Library, Massa- chusetts Institute of Technology. 242 I The most reasonable solution for moderate-size libraries is the use of con- sultants. However, a system analyst af- ter a little study, might argue that he could understand any system sufficiently to model its operation. Such a superfi- cial attitude might have impractical re- sults for the library system. This paper discusses the use of a li- brarian/ consultant team to model and study library operations. Without hiring a full-time analyst, this approach offers the advantage of applying systems tech- niques based on the assumptions and constraints explained by the librarian who has responsibility in the every day library system. The librarian has in- sights which the analyst cannot acquire in the few days normally available for observation. For example, the librarian is aware of the political constraints within the system which, as Churchman has pointed out, can be significant. 3 Be- sides the importance of the librarian scrutinizing the analyst's assumptions and methods, the participation of the library staff is imperative to implement the results of any study. 4 The most important aspect of using a librarian/ consultant team is the com- bination of viewpoints. As the librarian discusses how the particular library sys- tem operates, the analyst mentally for- l J 1 ~I Use of a Librarian/Consultant Team I 243 mulates the modeling approaches that seem applicable. The analyst then dis- cusses the assumptions necessary for particular models with the librarian. During such discussion, the individuals (who each have a different set of pro- fessional jargon) are forced to articu- late the exact meaning and limitations resulting from assumptions. AN EXAMPLE This example covers staffing of the in- formation desks at MIT's Humanities Library. 0 The study was self-initiated and often uses heuristic rather than ac- tual situations. Initially, the librarian and consultant talked about their re- spective roles in the study. 00 In this way, the librarian realized how much the consultant had to rely on the li- brarian's intuitive knowledge of the sys- tem's operation, particularly when large amounts of data could not be gathered. The team also discussed the credibility of a model's underlying assumptions. The purpose of information desks is to answer inquiries either by phone or in person regarding general locations and union catalog information. There are two information desks in the library facing the entrance, each providing equal access for inquirers. Two iden- tical telephone extensions are serviced by each desk. The schedule for manning the desks at the time of this study (Nov. 5-15, 1971) was roughly one person (for both desks) during the mornings and week- ends, and two people in the afternoons. The goal of this study was to determine if a schedule of staffing could be de- 0 The authors gratefully acknowledge the co- operation of Humanities Librarian F. B. B. Sumner and the help in collecting data of Li- brary AssistantS. Stillman. 0 0 In actuality, the consultant may not be dealing with the librarian, but with the individ- ual ( s) most involved with the particular system or subsystem being analyzed. For convenience, the term librarian is used in a generic rather than a professional sense. vised to provide acceptable service at lower costs. The librarian was able to point out areas of possible cost savings. Each in- formation librarian has other primary responsibilities that cannot be per- formed while on desk duty. Because in- formation-desk duty can interfere with an individual's other responsibilities, if each person could spend less time at the desks, then more time could be devoted to the primary areas of responsibility. Thus, without reducing staff size, this study proposed to increase output in other areas of library operation. A queuing model of the information desks system seemed natural and was the first approach pursued. The analyst asked if it was reasonable to assume that service times for the two popula- tions (i.e., phone and in-person in- quiries) could be aggregated into a sin- gle service time distribution. The li- brarian felt that phone inquiries, on the average, took considerably longer time to complete than in-person in- quiries. Thus, data was gathered by dis- tinguishing phone from in-person in- quiries. Data included the time between inquiry arrivals and the time it took to complete the service. It was soon found that few inquiries were made in the morning and on week- ends. Thus, this data was not analyzed because it was clear that an additional person was not needed at the .desks dur- ing those times. Also, the staffing could not be further reduced, since that would leave the unacceptable situation of no service at all. Hence, only t}:le data gathered during the afternoon was considered. Figures 1 and 2 show histograms of service times for phone inquiries, in- person inquiries, and interarrival times for each. To determine average inquiry rates ( A1 for phone inquiries and A2 for in-person inquiries) and average service rates ( /Ll for service of phone inquiries and J.L2 for service of in-per- 244 I College & Research Libraries • September 1973 100~-------------------------------------------------- - - - - :r,- PetuoH --PHONE. 20 0 +---~---.----;---~--~--~~~--~---~== 0 ' 8 10 .1.2 J:t .SE.RVIC£ HME (MIN) Histogram of Service Times Fig. 1 son inquiries), the data was replotted in Figure 3. Plotting the data and ana- lyzing as discussed by Morse, the fol- lowing were determined: A1 0.115 inquiries/minute A2 0.091 inquiries/minute J.A-1 0.331 services I minute p.-2 0.642 services I minute. 5 The ~A-'s are reasonably accurate and the difference between J.A- 1 and JA- 2 is consist- ent with the librarian's initial intuition. The ,\' s are definitely low. This is due to the inability to measure how often a phone inquirer found the two phones busy or how often an in-person inquirer was discouraged by seeing other inquir- ers waiting at the information desks for service. The team discussed this point thoroughly. The librarian could easily understand how the data originated: she collected it. However, for results to re- main credible to the librarian, the ana- lyst had to explain why he was going to "adjust" the data. The data is adjusted in either of the following ways: 1. A measurement must be made of how often both phones are busy, and how often both desks have sufficient in- person inquirers to discourage further inquirers. 2. The librarian must estimate these measurements. The situation dictated the second choice. Queue lengths must be assumed (infinity could be a choice). The librarian made the following deci- sions: a. In-person queue length of zero: no more than two inquirers will be at the information desks at one time. 0 0 0 0 0 0 Phone queue length necessarily equals zero. Use of a Librarian/Consultant Team I 245 ~0 24 r----, I I I I I I '-----! I I I I I I I I I ~----~ ~4~-'fJI -----+ 0+----~---~~----T---~---~---~---r-~---~----r----r---,----+-~r-~ 0 Histogram of Interarrival Times Fig. 2 b. Two phones are in use at the same time approximately three times per hour. c. Two in-person inquirers are at the desks at the same time approxi- mately two times per hour. The librarian and consultant agreed that if decisions b and c were to be biased, it should be in the direction of overestimating the load on the system. Thus, results using such estimates would be conservative with respect to decreas- ing staffing at the desks. With the above decisions and using discussion presented in Morse, a rela- tionship for estin1ating the actual ar- rival rate AT was derived. A AT - ( 1 - frequency of full queue) ( 1 ) p. Using ( 1) the data becomes (subscript T dropped for convenience) : At 0.136 A2 0.096 P-1 0.331 Jl-2 = 0.641 With these numerics, the system utiliza- tion p and average idle period 1/ A can be estimated. System utilization is the percentage of time the system is busy and is given by A p = 2p. ( for two servers ) . ( 2) A is the total inquiry rate given by A = At + A2 = 0.232, ( 3) and p. is the average service rate given by p. = (At ~ A2) p. + (At ~ A2) Jl-2 = 0.459. ( 4) Combining ( 2) through ( 4), p equals 0.253, which means that 75 percent of the time neither desk is servicing any 246 I College & Research Libraries • September 1973 7 .s;, (-t) S£RVtC£ 1iMI!. .DI3TIUaU110HS ----IN-PERsoN -PHoH£ 0 ~0 ;, = I A/ C t > c1t. A )o 'o ',,~7~0 (f.)•lHTIJWtRWAL TM£ DISTRIBUTIONS .......... ---- IN-P£R.SOH .... .... .... _-a. ....... - .......... r~ ..... .......... ......... -- ........ _ 40 Service and Interarrival Time Distributions Fig. 3 type of inquirer. The average period that this idle situation exists is 4.3 ·min- utes. For the purpose of comparison, if there were only one librarian on duty during this period, then p == ~ == 0.506. ( 5) p. :Nlorse suggests that p < 0.667 will yield library service that will not cause exces- sive delays. Thus, one librarian would be sufficient during the period analyzed. The single librarian will be much busier than with two librarians on duty. How- ever, if the total staff is tnaintained at its current size, each librarian would spend over 30 percent less time at the in- formation desks. These results pointed toward further applications of systems analysis data. In addition to data collection, the librarian was interested in other models that might yield more information about the system. A Markov model was discussed. 6 The following Markov model was proposed for further study of the in- formation desks system. The possible states of the system are listed in this Markov model: J Use of a Librarian/Consultant Team I 247 A Markov Model of the Information Desks System Fig. 4 State 1 2 3 4 5 6 7 8 9 Phones in use 0 0 0 1 1 1 2 2 2 In-Person inquirers 0 1 2 0 1 2 0 1 2 The model requires the probabilities of a transition from one state to another in a time interval ~t. As exponential service times and interarrival times have been implicitly assumed, it is known that at most one phone call and one in- person inquiry can occur in ~t. Using this property, the Markov model is illus- trated in Figure 4. The lines with ar- rows represent transitions between states. Note that some transitions are not possible. The probabilities of a transition can be more conveniently rep- resented with the following transition matrix. 1 2 3 4 5 6 7 8 9 lpu P12 Pta Pu P 1s 0 P11 0 0 1 I P21 P22 P23 P24, P25 P26 0 P28 0 2 0 P a2 P33 0 Pa5 P36 0 0 P ao 3 pu P 42 0 P« P45 p4,e P47 P 4s 0 4 P51 P 52 P53 PM Poo P56 P s7 P58 P59 5 ( 6 ) 0 Ps2 P63 0 P65 Pse 0 Pes Pso 6 0 0 0 P14, P1s 0 P11 P1s P1o 7 0 0 0 P84 Ps5 P86 Ps1 Pss Pso 8 2 0 0 0 Po5 P oo 0 Pos P oo 9 248 I College & Research Libraries • September 1973 where P1j = probability of a transition from state i to state j in time ~t. The zeroes in the above matrix came from the following facts: a. No more than two service opera- tions can be completed during ~t. b. No more than two inquiries (one phone, one in-person) can occur dur- ing ~t. If this study were pursued further the Pi/s could be determined. With the above matrix defined, the effects of vari- ous inquiry and service rates on system operation could be studied. CONCLUSION More time was spent in discussing the library system in general, what modeling has to offer, and the importance of as- sumptions, than in actually collecting and analyzing the data. The importance 1 of this process cannot be overestimated. j The librarian was not forced to learn the mathematics of modeling, but be- came an integral part of the modeling process as a librarian. The analyst gained information from the librarian that helped him avoid possible false ~ starts. He also benefited from the li- ~ brarian's enthusiasm, which might have emanated from the librarian's partici- pation in data collection. The actual work in the library re- quired approximately two days for the analyst and probably less for the librar- ians. This seems to be a small invest- ment for the recommendations derived, and perhaps more importantly, for the positive attitudes instilled in the librari- ans toward analysis of library opera- tions. REFERENCES 1. P. M. Morse, Library Effectiveness (Cam- bridge, Mass.: MIT Press, 1968); R. W. Burns, Jr., "A Generalized Methodology for Library Systems Analysis," CRL 32:295- 303 (July 1971); "Operations Research: Im- plications for Libraries," The Library Quar- terly 42 (Jan. 1972), entire issue. 2. F. F. Leimkuhler, "Library Operations Re- search: A Process of Discovery and Justifi- cation," The Library Quarterly 42:84-96 (Jan. 1972). 3. C. W. Churchman, "Operations Research Prospects for Libraries," The Library Quar- terly 42:6-14 (Jan. 1972). 4. E. A. Chapman, "Systems Study as Related to Library Operations: Need and Planning," Library Automat-ion, S. R. Salmon, ed. (Chi- cago: American Library As so cia tion, 1969 ) , p.7-12. 5. P. M. Morse, Queues, Inventories and Main- tenance (New York: Wiley, 1958), chapt. 2 .. 6. See A. W. Drake, Fundamentals of Applied Probability (New York: McGraw-Hill 1967), chapt. 5. '