State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems

State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems and Applications

State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems

We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing s...

State Space Collapse for Parallel Server Systems in Many-Server Limits

We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing s...

Approximations for Chat Service Systems Using Many-Server Diffusion Limits

We study a queueing model of customer service chat (CSC) systems. A unique feature of these queueing systems is that a single agent can serve multiple customers simultaneously. We prove the convergence of the queueing process to di↵erent di↵usion processes in a many server heavy-tra c regime in three di↵erent cases. Using this result, we are able o↵er approximations for the steady state perform...

Methods in Diffusion Approximation for Multi-Server Systems: Sandwich, Uniform Attraction and State-Space Collapse

In this chapter, we demonstrate through simple queueing models some of the methods that have been developed for the diffusion approximation. Specifically, we first show how the sandwich method is used to establish the diffusion approximation for a multi-server queue, and next show how the uniform attraction and the state-space collapse method is used to establish the diffusion approximation for...