Queueing Systems: Theory and Applications
State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
Strong approximations for Markovian service networks
Queueing Systems: Theory and Applications
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Mathematics of Operations Research
A Diffusion Approximation for the G/GI/n/m Queue
Operations Research
Heavy-Traffic Limits for the G/H2*/n/m Queue
Mathematics of Operations Research
Optimal Routing In Output-Queued Flexible Server Systems
Probability in the Engineering and Informational Sciences
Maximum Pressure Policies in Stochastic Processing Networks
Operations Research
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Contact Centers with a Call-Back Option and Real-Time Delay Information
Operations Research
Optimal control of parallel server systems with many servers in heavy traffic
Queueing Systems: Theory and Applications
Service-Level Differentiation in Call Centers with Fully Flexible Servers
Management Science
Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime
Mathematics of Operations Research
Multiserver Loss Systems with Subscribers
Mathematics of Operations Research
Fundamentals of Queueing Theory
Fundamentals of Queueing Theory
Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
A Fluid Approximation for Service Systems Responding to Unexpected Overloads
Operations Research
Robust Design and Control of Call Centers with Flexible Interactive Voice Response Systems
Manufacturing & Service Operations Management
Estimating the loss probability under heavy traffic conditions
Computers & Mathematics with Applications
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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-Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in this regime for parallel server systems. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a “state space collapse” function, which governs the exact details of the state space collapse. We show that a state space collapse result holds in many-server heavy traffic if a corresponding deterministic hydrodynamic model satisfies a similar state space collapse condition. Unlike the single-server heavy traffic setting for multiclass queueing network, our hydrodynamic model is different from the standard fluid model for many-server queues. Our methodology is similar in spirit to that in Bramson [Bramson, M. 1998. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems30 89--148.], which focuses on the single-server heavy traffic regime. We illustrate the applications of our results by establishing state space collapse results in many-server diffusion limits for V-model systems under static-buffer-priority policy and the threshold policy proposed in the literature.