Exact asymptotics in an infinite-server system with overdispersed input

TL;DR

This paper derives exact tail asymptotics for the number of customers in an infinite-server system with overdispersed input, using a change-of-measure approach under specific scaling, supported by illustrative examples.

Contribution

It provides the first precise asymptotic analysis of overdispersed input in infinite-server queues, extending existing models with exact tail behavior results.

Findings

Exact tail asymptotics derived for overdispersed input

Change-of-measure technique applied for proofs

Illustrative examples demonstrate applicability

Abstract

This short communication considers an infinite-server system with overdispersed input. The objective is to identify the exact tail asymptotics of the number of customers present at a given point in time under a specific scaling of the model (which involves both the arrival rate and time). The proofs rely on a change-of-measure approach. The results obtained are illustrated by a series of examples.