Robust heavy-traffic approximations for service systems facing overdispersed demand

TL;DR

This paper develops scalable heavy-traffic approximations for service systems with overdispersed demand, leading to improved capacity sizing rules and robust performance estimates for moderate-sized or non-heavy traffic systems.

Contribution

It introduces novel heavy-traffic approximations tailored for overdispersed demand, enhancing capacity planning and performance analysis in such systems.

Findings

Derivation of scalable heavy-traffic approximations for overdispersed demand

Development of new capacity sizing rules accounting for overdispersion

Robust performance estimates for systems not in heavy traffic

Abstract

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic.