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

2025/09/17 by Amir Alwan, Alwan, Amir A., Barış Ata +1
Business, Management and Accounting · Decision Sciences · Engineering · #Advanced Queuing Theory Analysis #Probability and Risk Models #Advanced Wireless Network Optimization

paper · pdf · doi:10.48550/arxiv.2509.13748

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\unicodex2014where the number of jobs and single-server service rates grow large while infinite-server rates remain fixed\unicodex2014we prove a weak convergence result for the queue length and idleness process vector, providing an approximation for the original system.

Citations

• Dynamic control of stochastic matching systems in heavy traffic: An effective computational method for high-dimensional problems
• Analysis and Improvement of Eviction Enforcement
• Singular Control of (Reflected) Brownian Motion: A Computational Method Suitable for Queueing Applications
• Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Regime: A Computational Approach for High-Dimensional Problems
• A Queueing Model of Dynamic Pricing and Dispatch Control for Ride-Hailing Systems Incorporating Travel Times
• Empty-car routing in ridesharing systems
• A broader view of Brownian networks

Related

• Many-Server Heavy-Traffic Limits for Queueing Systems with Perfectly Correlated Service and Patience Times
• Heavy-traffic approximations for a layered network with limited\n resources
• Heavy traffic limit of stationary distribution of the multi-level single server queue
• Stationary Distribution Convergence of the Offered Waiting Processes in Heavy Traffic under General Patience Time Scaling
• Heavy traffic limit with discontinuous coefficients via a non-standard semimartingale decomposition