It is generally accepted that operating with a combined (i.e., pooled) queue rather than separate (i.e., dedicated) queues is beneficial 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 multiserver queueing system that 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; they are not subject to an external admission control. In this setting, we prove that, contrary to the common understanding, pooling queues can increase the long-run average sojourn time so much 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 hurts performance when the arrival-rate-to-service-rate ratio is large (e.g., greater than one) and the normalized service benefit is also large. We prove that the performance loss due to pooling queues can be significant. Our numerical studies demonstrate that pooling queues can decrease the social welfare (and consumer surplus) by more than 95%. The benefit of pooling is commonly believed to increase with system size. In contrast, we show 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. This paper was accepted by Terry Taylor, operations management.
Processor-sharing and random-service queues with semi-Markovian arrivals
