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

Amir A. Alwan; Barış Ata

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arXiv · 2509.13748

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

Amir A. Alwan·Barış Ata

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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.

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BibTeX RIS

Amir A. Alwan, Barış Ata. 2025-09-17. Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations. https://arxiv.org/abs/2509.13748

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