perspectives on queues: combining queues is not always beneficial

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Perspectives on Queues: Combining Queues is Not Always Beneficial Author(s): Michael H. Rothkopf and Paul Rech Source: Operations Research, Vol. 35, No. 6 (Nov. - Dec., 1987), pp. 906-909 Published by: INFORMS Stable URL: http://www.jstor.org/stable/171440 . Accessed: 09/05/2014 11:48 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . INFORMS is collaborating with JSTOR to digitize, preserve and extend access to Operations Research. http://www.jstor.org This content downloaded from 195.78.109.186 on Fri, 9 May 2014 11:48:58 AM All use subject to JSTOR Terms and Conditions

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Page 1: Perspectives on Queues: Combining Queues is Not Always Beneficial

Perspectives on Queues: Combining Queues is Not Always BeneficialAuthor(s): Michael H. Rothkopf and Paul RechSource: Operations Research, Vol. 35, No. 6 (Nov. - Dec., 1987), pp. 906-909Published by: INFORMSStable URL: http://www.jstor.org/stable/171440 .

Accessed: 09/05/2014 11:48

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

INFORMS is collaborating with JSTOR to digitize, preserve and extend access to Operations Research.

http://www.jstor.org

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Page 2: Perspectives on Queues: Combining Queues is Not Always Beneficial

PERSPECTIVES ON QUEUES: COMBINING QUEUES IS NOT ALWAYS BENEFICIAL

MICHAEL H. ROTHKOPF University of California, Berkeley, California

PAUL RECH San Francisco State University, San Francisco, California

(Received February 1987; revision received September 1987; accepted September 1987)

Contrary to common calculation, there are reasons for believing that combining queues, especially queues of people, may at times be counterproductive. These reasons include customer reaction, jockeying between separate queues, increased costs and service times for combined queues, and the absence of published before-and-after studies.

A recent seminar given by a panel of faculty in the operations research department of a major

university had as its theme the value of operations research. One participant cited the practice of combin- ing separate queues as a major and obvious example of the benefits that can accrue from the use of opera- tions research techniques. Another pointed out that, while many banks and other counter systems have gone to combined queues, many managers have been slow to adopt this obvious improvement and that the operations research community should devote more effort to "selling" the practice.

A member of the audience, a graduate of the de- partment who is now employed in industry, was the only one to raise a caution. He suggested that man- agers might be reluctant to combine queues because of concern about customer acceptance; the combined queue looks longer. This comment was taken as indi- cating that those who needed "education" might be the customers, not the managers. No one at the sem- inar asked the obvious question: is combining queues, in fact, a good idea? And, are there factors, other than customer ignorance, that ought to lead one to question the benefits of combining queues-especially queues of people? It is the purpose of this article to suggest that such factors do exist and that they deserve careful investigation. First, however, for completeness, we set forth the case for combining queues.

The Argument for Combining Queues

For Markovian queues, it is a simple matter to com- pare the steady-state average wait for two systems:

(i) s standard (i.e., first-come-first-served, unlim- ited waiting room, no balking or reneging)

M/M/1 systems having service rate A and arrival rate X, and

(ii) a standard M/M/s system with the same service rate A and a corresponding arrival rate sX.

This comparison will always show that the average wait is less for the second system for any positive X and any integer s > 1. Smith and Whitt (1981) give a proof. Indeed, the improvement can be substantial. Wolff's forthcoming book (1988) shows that the av- erage wait in the combined queue is less by at least a factor of s. A similar comparison for the variance of the wait in the system leads to a similar result. Fur- thermore, similar comparisons involving various non- Markovian queues will yield similar results. Wolff (1977, 1987, 1988), as well as Smith and Whitt, give some relevant proofs. Indeed, introductory texts often discuss comparisons such as these. For example, see Wagner (1975, pp. 882-883) or Baker and Kropp (1985, p. 474). Hillier and Lieberman (1974) present an extensive example involving the combining of geo- graphically dispersed servers. Other texts assign stu- dents the task of modeling simple comparisons. For example, see Trueman (1977), problem 12.12; Ander- son and Lievano (1976), problem 8-4; or Davis, McKeown and Raher (1986), problem 20-13. Bier- man, Bonini and Hausman (1986), problems 20-5 and 20-13 assign such comparisons with appropriate calls for examination of assumptions.

Combining Queues Might Not Be Advantageous

Do such comparisons or proofs settle the matter? No, and for several reasons, some of which are related to the fact that independent, single queues may not be the real alternative to combined queues.

Subject classification: 683 considerations in combining queues of people, 696, 699 considerations in combining queues in practice.

Operations Research 0030-364X/87/3506-0906 $01.25 Vol. 35, No. 6, November-December 1987 906 ? 1987 Operations Research Society of America

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First, all of the reduction in workload (measured in server minutes) waiting for service occurs because with s independent M/M/l systems a customer sometimes must wait for one server while another server is idle, a situation that does not occur in a single M/M/s system. In most real queues involving people, how- ever, customers seldom wait for one server while another is idle ("No waiting on Aisle 7"). Comparing s separate queues with jockeying, at least when a server is idle, to the single queue M/M/s system leads to different results. If the jockeying is nondiscriminatory with respect to waiting time, then the number of customers in the queue and, hence, the average wait in the queue will be the same in both types of systems. Moreover, if the jockeying favors shorter jobs, then the average wait will be less in the separate queue system. Shorter jobs might be favored because such customers can jockey more effectively (for example, those with baskets vs. those with full shopping carts), or because cultural factors such as politeness favor letting customers with short jobs be served first. Even if the jockeying is nondiscriminatory with respect to service time, it may reduce average delay costs if those in a hurry due to high delay costs are more prone to jockey.

Even with jockeying that is nondiscriminatory with respect to service time, the average wait in the single queue system will be longer if for any reason combin- ing the queues increases the service times even slightly. There are several possible reasons why such increases might occur. It may take time to get from the central queue to the next available server. It may be that the physical proximity of the customer to his or her ulti- mate server can allow some overlapping of service such as unloading a shopping cart or getting a form to fill out while the current customer signs one. It may also be that a server is more accountable and feels more responsible for his or her own queue and may therefore be inclined to work faster, especially when the queue is long. With individual queues, customers "belong" to individual servers, and therefore, a server cannot easily rely on other servers to take care of his or her customers. Finally, it may also be faster because of a subtle degree of specialization. If I usually use the same teller, that teller may become more efficient in dealing with my typical transactions.

While jockeying will not eliminate all of the differ- ence in the variance of time in the system, it will reduce some of the variance in the multi-queue case. On the other hand, any increase in service time for any of the reasons discussed above will increase the variance as well as the mean time in the system in the

single queue situation. When server utilization is high, this can be a dominating effect.

Even if there is no jockeying, if customers tend to join shorter queues, the separate systems are no longer independent; such behavior by arrivals would elimi- nate much of the extra delay of independent systems. In particular, if arriving customers can observe accu- rately the workload in each separate queue and then join the queue with the shortest workload, the distri- bution of delays will be the same as it would be with a combined queue. If arriving customers join the queue with the fewest customers, the result is almost as good. The less variability there is in service times, and the longer the queues, the more accurately the number of customers in a queue predicts that queue's workload. This result suggests that practices that tend to reduce the variance in service times-especially the unobservable part of the variance-are not only effec- tive tools in the management of queuing systems, but also reduce the incentive to combine queues.

Even if service times do not change and there is no jockeying, if the separate queues tend to segregate jobs by service time (as with an express line), combining the queues will increase the variance of the service times in the combined queue and may increase aver- age delay. Smith and Whitt give examples to illustrate this effect.

Going to a single queue system may involve a variety of disadvantages. First, it makes it more diffi- cult for customers to choose servers and, thus, may contribute to depersonalizing the server-customer re- lationship and decreasing the customer's sense of sat- isfaction and perhaps the server's as well. Second, it makes it difficult for the system to use opportunities for partially specialized servers ("Money orders at windows 5, 6, or 7 only"), forcing it to incur the additional cost of training and equipping each server for each allowed type of service. An important kind of specialization is geographic dispersion. Of course, combined queues within a specialization may be worth considering, but then subspecialization is ruled out. Third, it may deprive management of an oppor- tunity to use delay avoidance to motivate customer behavior it desires ("Cash only in the express line;" "Diamond lanes for car pools only"). Finally, it may focus scarce managerial attention on a relatively un- important question. The critical question regarding the queue's management may well be the rules for adding or subtracting servers (e.g., by sending them to stock shelves or sort letters), the rules for assigning priorities, the selection of equipment for increasing the speed of servers, procedures for reducing the

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variance of service times (e.g., allocating bagging as- sistance), or improving the quality of the experience and the satisfaction of customers while waiting.

Finally, we have another reason for questioning the efficiency in practice of combining queues. While much successful OR practice is not reported, we have seen a number of papers on the successful application of queueing theory. Papers by Edie (1954), Bouland (1967), Koopman (1972), Bleuel (1975), Gilliam (1979), McKeown (1979), Rothkopf and Oren (1979), Vogel (1979), and Sze (1984), and the work of the New York City RAND Institute come to mind. But we do not recall seeing a convincing practice paper describing a successful unification of a multiqueue system into a single queue system. Bleuel's paper that won the 1974 prize for practice from the College on The Practice of Management Science comes closest. It analyzes service team size for a geographically dis- persed service operation and recommends medium size teams. A paper by Jones, Oberski and Tour (1980) discusses a survey of shopper attitudes toward com- bining grocery store queues and ends up with a slightly negative attitude toward such combining, based, in part, upon the fact that it eliminates jockeying.

In a recent paper, Larson (1987) argues that the psychological experiences of people in queues may be more important than the actual amount of delay. In particular, he argues that the perceived "social injus- tice" of the violation of first-come-first-served order may contribute to dissatisfaction. Of course, com- bined queues avoid violations of the first-come-first- served order. We heartily agree with Larson's views on the importance of the psychology of queueing. We also agree that perceptions of fairness can play a role. Queue managers, however, may be clever enough to deal with this aspect of the problem without seriously compromising other aspects of the operational effec- tiveness of the system. Furthermore, the power to choose a server and to jockey may be an important psychological benefit that helps to offset the sense of powerlessness that waiting can cause. It may also reduce feelings of frustration and injustice associated with violations of the first-come-first-served order.

Summary

In summary, there are significant reasons for believing that combining queues may at times not be a good thing to do. These reasons include customer reaction, elimination of jockeying, increased service times and costs for combined queues, and the absence of pub- lished before-and-after studies. Of course, this is not to say that combining queues is always a bad idea. We

are confident that in many engineering contexts in which arrivals cannot jockey, it is a manifestly good idea. It may also be advantageous in a number of counter service systems. However, it is not automati- cally a winner.

We hope that when operations researchers think about and analyze service systems, they will pay atten- tion to the concerns we have raised. In addition, we hope that some of these concerns will inspire new research on queueing questions and will encourage publication of careful reports of experience in com- bining queues in counter service systems.

Acknowledgment

We are indebted for perceptive comments by two anonymous referees, as well as by Fred Hillier, Ernest Koenigsberg, Ronald Wolff, David Wood, and espe- cially Ward Whitt.

References

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BAKER, K. R., AND D. H. KROPP. 1985. Management Science: An Introduction to the Use of Decision Models. John Wiley & Sons, New York.

BIERMAN, H., JR., C. P. BONINI AND W. H. HAUSMAN.

1986. Quantitative Analysis for Business Decisions, Ed. 7. Irwin, Homewood, Ill.

BLEUEL, W. H. 1975. Management Science's Impact on Service Strategy. Interfaces 6, 4-12.

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DAVIS, K. R., P. G. MCKEOWN AND T. R. RAHER. 1986. Management Science: An Introduction, Kent Pub- lishing, Boston.

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