On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times

TL;DR

This paper analyzes the tail behavior of the stationary sojourn time in a tandem queue system with light-tailed service times, revealing that large sojourn times are mainly caused by a single large service time, and provides elementary proofs for asymptotics.

Contribution

It offers a detailed asymptotic analysis of the stationary sojourn time in tandem queues with light-tailed distributions, including elementary proofs for tail asymptotics.

Findings

Large sojourn times are mostly due to a single large service time.

Provides elementary proof of logarithmic tail asymptotics.

Identifies an 'intermediate' region where tail behavior is dominated by individual service times.

Abstract

We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that, in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value mostly due to a large value of a single service time of one of customers. Arguments used in the paper allow us to obtain also an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions.