Queueing Systems When Customers Can Balk: Pooled or Dedicated?

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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.