Queues with service resetting

TL;DR

This paper develops a comprehensive theory for queues with service resetting, considering independent sources of service time variability, and identifies conditions under which resetting improves queue performance.

Contribution

It introduces a new theoretical framework for $S ext{ extasciitilde}X$ queues with service resetting, analyzing cases with sum or product of service components, and evaluates resetting policies.

Findings

Resetting can reduce mean service time under certain conditions.

Explicit expressions for service time distribution and queue metrics are derived.

Numerical simulations confirm the analytical results.

Abstract

Service time fluctuations heavily affect the performance of queueing systems, causing long waiting times and backlogs. Recently, it was shown that when service times are solely determined by the server, service resetting can mitigate the deleterious effects of service time fluctuations and drastically improve queue performance (Bonomo et al.,2022). Yet, in many queueing systems, service times have two independent sources: the intrinsic server slowdown ($S$) and the jobs' inherent size ($X$). In these, so-called $S\&X$ queues (Gardner et al., 2017), service resetting results in a newly drawn server slowdown while the inherent job size remains unchanged. Remarkably, resetting can be useful even then. To show this, we develop a comprehensive theory of $S\&X$ queues with service resetting. We consider cases where the total service time is either a product or a sum of the service slowdown and the jobs' inherent size. For both cases, we derive expressions for the total service time distribution and its mean under a generic service resetting policy. Two prevalent resetting policies are discussed in more detail. We first analyze the constant-rate (Poissonian) resetting policy and derive explicit conditions under which resetting reduces the mean service time and improves queue performance. Next, we consider the sharp (deterministic) resetting policy. While results hold regardless of the arrival process, we dedicate special attention to the $S\&X$-M/G/1 queue with service resetting, and obtain the distribution of the number of jobs in the system and their sojourn time. Our analysis highlights situations where service resetting can be used as an effective tool to improve the performance of $S\&X$ queueing systems. Several examples are given to illustrate our analytical results, which are corroborated using numerical simulations.