Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations
Probability
2026-03-13 v4
Abstract
This paper studies the limiting behavior of a closed queueing network with multiple single-server and infinite-server stations. Under a heavy traffic asymptotic regimewhere the number of jobs and single-server service rates grow large while infinite-server rates remain fixedwe prove a weak convergence result for the queue length and idleness process vector, providing an approximation for the original system.
Keywords
Cite
@article{arxiv.2509.13748,
title = {Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations},
author = {Amir A. Alwan and Barış Ata},
journal= {arXiv preprint arXiv:2509.13748},
year = {2026}
}