Stochastic Systems

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

J. G. Dai and Shuangchi He

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1393251982

Digital Object Identifier
doi:10.1214/11-SSY029

Mathematical Reviews number (MathSciNet)
MR3353469

Zentralblatt MATH identifier
1296.60243

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.ssy/1393251982


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