Poisson Hypothesis for Information Networks (A study in non-linear Markov processes) I. Domain of Validity

TL;DR

This paper investigates the Poisson Hypothesis in large queueing networks, proving its validity in certain cases by analyzing non-linear Markov processes and identifying conditions where it may fail, especially with heavy-tail service times.

Contribution

It establishes the domain of validity for the Poisson Hypothesis using non-linear Markov process analysis and explores conditions leading to its violation.

Findings

The dynamical system has a line of fixed points that are global attractors.

The Poisson Hypothesis holds in certain limiting cases.

Heavy-tail service times can violate the Poisson Hypothesis.

Abstract

In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queueing networks. We prove it in some simple limiting cases. We show in particular that the corresponding dynamical system, defined by the non-linear Markov process, has a line of fixed points which are global attractors. To do this we derive the corresponding non-linear equation and we explore its self-averaging properties. We also argue that in cases of havy-tail service times the PH can be violated.