Pooled versus Dedicated Queues When Customers Are Delay-Sensitive

72 Pages Posted: 26 Jul 2017 Last revised: 27 Jan 2020

See all articles by Nur Sunar

Nur Sunar

University of North Carolina (UNC) at Chapel Hill - Kenan-Flagler Business School

Yichen Tu

University of North Carolina (UNC) at Chapel Hill

Serhan Ziya

Department of Statistics and Operations Research

Date Written: July 17, 2017

Abstract

It is generally accepted that operating with a combined (i.e., pooled) queue rather than separate (i.e., dedicated) queues is beneficial mainly because pooling queues reduces long-run average sojourn time. In fact, this is a well-established result in the literature when jobs cannot make decisions and servers and jobs are identical. An important corollary of this finding is that pooling queues improves social welfare in the aforementioned setting. We consider an observable multi-server queueing system which can be operated with either dedicated queues or a pooled one. Customers are delay-sensitive and they decide to join or balk based on queue length information upon arrival. In this setting, we prove that, contrary to the common understanding, pooling queues can considerably increase the long-run average sojourn time so that the pooled system results in strictly smaller social welfare (and strictly smaller consumer surplus) than the dedicated system under certain conditions. Specifically, pooling queues leads to performance loss when the arrival-rate-to-service-rate ratio and the normalized benefit of service are both large. We also prove that performance loss due to pooling queues can be significant. Our numerical studies demonstrate that pooling queues can decrease the social welfare (and the consumer surplus) by more than 95%. The benefit of pooling is commonly believed to increase with the system size. In contrast to this belief, our analysis shows that when delay-sensitive customers make rational joining decisions, the magnitude of the performance loss due to pooling can strictly increase with the system size.

Keywords: pooled queue, dedicated queues, customer balking, rational customers, delay-sensitive customers, observable queues

Suggested Citation

Sunar, Nur and Tu, Yichen and Ziya, Serhan, Pooled versus Dedicated Queues When Customers Are Delay-Sensitive (July 17, 2017). Available at SSRN: https://ssrn.com/abstract=3007374 or http://dx.doi.org/10.2139/ssrn.3007374

Nur Sunar (Contact Author)

University of North Carolina (UNC) at Chapel Hill - Kenan-Flagler Business School ( email )

McColl Building
Chapel Hill, NC 27599-3490
United States

Yichen Tu

University of North Carolina (UNC) at Chapel Hill ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

Serhan Ziya

Department of Statistics and Operations Research ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

HOME PAGE: http://www.unc.edu/~ziya/

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