Heavy tails in multi-server queues

TL;DR

This paper investigates the tail behavior of waiting times and workloads in a two-server queue, providing bounds and asymptotics under subexponential service time assumptions, highlighting the impact of traffic load.

Contribution

It offers new asymptotic results for the tail distributions in a $GI/GI/2$ queue, extending understanding of heavy-tailed phenomena in multi-server systems.

Findings

Derived bounds for tail probabilities of waiting times

Established sharp asymptotics under subexponential assumptions

Showed dependence of tail behavior on traffic load

Abstract

In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time $W$ in the $GI/GI/2$ FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability ${\bf P}\{W>x\}$. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary queue length. These asymptotics depend heavily on the traffic load.