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, thus 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 favorable advantage. This happens when stochastic fluctuations are intrinsic to the server, and we show that service resetting can then dramatically cut down average queue lengths and waiting times. Remarkably, this strategy is also useful in extreme situations where the variance, and possibly even mean, of the service time diverge—as resetting can then prevent queues from "blowing up."We illustrate these results on the M/G/1 queue in which service times are general and arrivals are assumed to be Markovian. However, the main results and conclusions coming from our analysis are not specific to this particular model system. Thus, the results presented herein can be carried over to other queueing systems: in telecommunications, via computing, and all the way to molecular queues that emerge in enzymatic and metabolic cycles of living organisms.