Ph.D. Defense: Yichen Tu
The Department of
Statistics and Operations Research
The University of North Carolina at Chapel Hill
Queuing Systems with Strategic and Learning Customers
(Under the direction of Serhan Ziya and Nur Sunar)
In many service systems customers are strategic and can make their own decisions. In particular, customers can be delay-sensitive and they will leave the system if they think the waiting time is too long. For the service provider, it is important to understand customers’ behaviors and choose the appropriate system design. This dissertation consists of two research projects.
The first project studies the pooling decision when customers are strategic. 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 relative 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.
The second project studies the learning behavior when customers don’t have full information of the service speed. We consider a single-server queueing system where customers make join- ing and abandonment decisions when the service rate is unknown. We study different ways in which customers process service-related information, and how these impact the performance of a service provider. Specifically, we analyze forward-looking, myopic and naive information process- ing behaviors by customers. Forward-looking customers learn about the service rate in a Bayesian framework by using their observations while waiting in the queue. Moreover, they make their abandonment decisions considering both belief and potential future payoffs. On the other hand, naive customers ignore the available information when they make their decisions. We prove that regardless of the way in which the information is processed by customers, a customer’s optimal joining and abandonment policy is of threshold-type. There is a rich literature that establishes that forward-looking customers are detrimental to a firm in settings different than queueing. In contrast to this common understanding, we prove that for service systems, forward-looking customers are beneficial to the firm under certain conditions.