English

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 regime\unicodex2014\unicode{x2014}where the number of jobs and single-server service rates grow large while infinite-server rates remain fixed\unicodex2014\unicode{x2014}we 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}
}
R2 v1 2026-07-01T05:41:20.148Z