Many-server Queues with Customer Abandonment: Numerical Analysis of their Diffusion Model

Jim G. Dai · Shuangchi He

60 citations0/0 files storedStochastic Systems

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

We use a multidimensional diffusion process to approximate the dynamics of a queue served by many parallel servers. Waiting customers in this queue may abandon the system without service. To analyze the diffusion model, we develop a numerical algorithm for computing its stationary distribution. A crucial part of the algorithm is choosing an appropriate reference density. Using a conjecture on the tail behavior of the limit queue length process, we propose a systematic approach to constructing a reference density. With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments. These experiments demonstrate that the diffusion model is a satisfactory approximation for many-server queues, sometimes for queues with as few as twenty servers.

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References

1987Stochastic Differential Equations: An Introduction with Applications.2003Stochastic Differential Equations 1999Introduction to Matrix Analytic Methods in Stochastic Modeling 2005Statistical Analysis of a Telephone Call Center 1981Heavy-Traffic Limits for Queues with Many Exponential Servers 2002Designing a Call Center with Impatient Customers 1984Open Queueing Networks in Heavy Traffic 1970Multiple channel queues in heavy traffic. II: sequences, networks, and batches

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2018Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems 2014Validity of heavy-traffic steady-state approximations in many-server queues with abandonment 2011Queues in Service Systems: Customer Abandonment and Diffusion Approximations 2021SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers

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