Open Access
2013 Many-server queues with customer abandonment: Numerical analysis of their diffusion model
J. G. Dai, Shuangchi He
Stoch. Syst. 3(1): 96-146 (2013). DOI: 10.1214/11-SSY029


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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J. G. Dai. Shuangchi He. "Many-server queues with customer abandonment: Numerical analysis of their diffusion model." Stoch. Syst. 3 (1) 96 - 146, 2013.


Published: 2013
First available in Project Euclid: 24 February 2014

zbMATH: 1296.60243
MathSciNet: MR3353469
Digital Object Identifier: 10.1214/11-SSY029

Primary: 60J70 , 60K25 , 65R20
Secondary: 68M20

Keywords: customer abandonment , diffusion process , heavy traffic , Many-server queue , phase-type distribution , quality- and efficiency-driven regime , stationary distribution

Rights: Copyright © 2013 INFORMS Applied Probability Society

Vol.3 • No. 1 • 2013
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