Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations

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$\unicode{x2014}$where the number of jobs and single-server service rates grow large while infinite-server rates remain fixed$\unicode{x2014}$we prove a weak convergence result for the queue length and idleness process vector, providing an approximation for the original system.