A stochastic network with mobile users in heavy traffic

TL;DR

This paper analyzes a stochastic network with mobile users under heavy traffic, deriving scaling limits, proving spatial state space collapse, and establishing convergence of stationary distributions and sojourn times.

Contribution

It introduces a novel approach to analyze heavy-traffic limits in mobile user networks using excursion-based convergence methods.

Findings

Derived the scaling limit of the queue length process.

Proved spatial state space collapse in the network.

Established weak convergence of stationary distributions.

Abstract

We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by Lambert and Simatos which provides a general principle to establish scaling limits of regenerative processes based on the convergence of their excursions. We also prove weak convergence of the sequences of stationary joint queue length distributions and stationary sojourn times.