Queues with service resetting
研究了服务时间由服务器慢速和任务固有大小共同决定的S&X排队系统，推导了服务重置策略下总服务时间分布和均值的表达式，给出了降低平均服务时间并改善排队性能的条件。
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. • Service resetting can improve the performance of queueing systems. • Our findings apply to S&X queues, covering regular queues as a special case. • Explicit conditions for resetting to reduce the mean service time are derived. • Conditions guide the efficient implementation of service resetting. • Our results apply regardless of the arrival process to the queue.