Resetting-induced instability in queues fed by a search process in an interval

TL;DR

This paper investigates how stochastic resetting in search processes affects the stability and convergence of resource queues, revealing a threshold resetting rate that influences system behavior.

Contribution

It combines queuing theory with search processes with stochastic resetting to identify parameter regions ensuring queue stability and analyzes the impact of resetting rate thresholds.

Findings

Identifies parameter regions for queue convergence with resetting.

Finds a threshold resetting rate that shifts the effect of resetting.

Shows exponential growth of the threshold with the number of servers.

Abstract

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival distribution is determined by a search process with stochastic resetting. When the queuing system has a limited number of servers and the search process occurs within a bounded domain, the dynamics of expediting or delaying the search through stochastic resetting interact with the long-term dynamics of the number of resources in the queue. We combine results from queuing theory with those from search processes with stochastic resetting in a bounded domain to obtain regions of the parameter space of the search process that ensure convergence of the number of resources in the queue to a steady state. Furthermore, we find a threshold resetting rate at which the effects of stochastic resetting shift from reducing convergence regions to expanding them. Finally, we demonstrate that this threshold value grows exponentially with the number of servers, making it harder for stochastic resetting to improve the convergence of the queueing system.