Heavy tails in multi-server queues
Sergey Foss, Dmitry Korshunov

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 in the FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability . 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.
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Probability and Risk Models · Random Matrices and Applications
