A polling system whose stability region depends on a whole distribution of service times

TL;DR

This paper introduces a single-server polling system with an adaptive policy where stability depends on the entire service time distribution, including an exponential moment, challenging traditional fluid approximation methods.

Contribution

It demonstrates that the stability region can depend on complex distributional properties, highlighting limitations of fluid approximation in such models.

Findings

Stability depends on the entire service time distribution.

Fluid approximation may not accurately predict stability.

Exponential moments influence the system's stability region.

Abstract

We present an example of a single-server polling system with two queues and an adaptive service policy where the stability region depends on the expected values of all the primitives and also on a certain exponential moment of the service-time distribution in one of the queues. The latter parameter can not be determined, in general, in terms of any finite number of power moments. It follows that the fluid approximation approach may not be an appropriate tool for the stability study of this model.