Mitigating long queues and waiting times with service resetting

Abstract

What determines the average length of a queue which stretches in front of a service station? The answer to this question clearly depends on the average rate at which jobs arrive at the queue and on the average rate of service. Somewhat less obvious is the fact that stochastic fluctuations in service and arrival times are also important, and that these are a major source of backlogs and delays. Strategies that could mitigate fluctuations induced delays are in high demand as queue structures appear in various natural and man-made systems. Here we demonstrate that a simple service resetting mechanism can reverse the deleterious effects of large fluctuations in service times, thus turning a marked drawback into a favourable advantage. This happens when stochastic fluctuations are intrinsic to the server, and we show that the added feature of service resetting can then dramatically cut down average queue lengths and waiting times. While the analysis presented herein is based on the M/G/1 queueing model where service is general but arrivals are assumed to be Markovian, Kingman's formula asserts that the benefits of service resetting will carry over to queues with general arrivals. We thus expect results coming from this work to find widespread application to queueing systems ranging from telecommunications, via computing, and all the way to molecular queues that emerge in enzymatic and metabolic cycles of living organisms.

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