Non-Markovian state dependent networks in critical loading

TL;DR

This paper develops heavy traffic limit theorems for critically loaded queueing networks with non-Markovian, state-dependent dynamics, resulting in a reflected process limit and applications to generalized Jackson networks.

Contribution

It introduces heavy traffic limits for non-Markovian, state-dependent queueing networks, extending classical models to more complex, realistic systems.

Findings

Established heavy traffic limit theorems for non-Markovian networks.

Derived the limit process as a reflected continuous-path process.

Applied results to generalized Jackson networks with state-dependent rates.

Abstract

We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state dependence. The limit stochastic process is a continuous-path reflected process on the nonnegative orthant. We give an application to generalised Jackson networks with state-dependent rates.