Stochastic Systems

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

J. G. Dai and Shuangchi He

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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.

Article information

Stoch. Syst., Volume 3, Number 1 (2013), 96-146.

First available in Project Euclid: 24 February 2014

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 65R20: Integral equations
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

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


Dai, J. G.; He, Shuangchi. Many-server queues with customer abandonment: Numerical analysis of their diffusion model. Stoch. Syst. 3 (2013), no. 1, 96--146. doi:10.1214/11-SSY029.

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