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Many-server queues with customer abandonment: Numerical analysis of their diffusion model

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Author(s): Shuangchi He | Jim Dai

Journal: Stochastic Systems
ISSN 1946-5238

Volume: 3;
Issue: 1;
Start page: 97;
Date: 2013;
Original page

Keywords: Diffusion process | stationary distribution | phase-type distribution | many-server queue | heavy traffic | customer abandonment | quality- and efficiency-driven regime

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