On large queue lengths in generalised Jackson networks

TL;DR

This paper establishes a large deviation principle for the stationary queue length distribution in subcritical generalized Jackson networks, providing a theoretical foundation for understanding rare events in such queueing systems.

Contribution

It proves an LDP for queue lengths in generalized Jackson networks under Cramer conditions, linking the deviation function to the quasipotential.

Findings

Large deviation principle established for queue lengths

Deviation function characterized by quasipotential

Applicable under Cramer condition on interarrival and service times

Abstract

This paper proves a large deviation principle (LDP) for the stationary distribution of queue lengths in a subcritical generalised Jackson network assuming a Cramer condition on the interarrival and service times. The deviation function is given by the quasipotential.