MAP/M/c and M/PH/c queues with constant impatience times

Ken’ichi Kawanishi () and Tetsuya Takine ()
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Ken’ichi Kawanishi: Gunma University
Tetsuya Takine: Osaka University

Queueing Systems: Theory and Applications, 2016, vol. 82, issue 3, No 5, 420 pages

Abstract: Abstract This paper considers stationary MAP/M/c and M/PH/c queues with constant impatience times. In those queues, waiting customers leave the system without receiving their services if their elapsed waiting times exceed a predefined deterministic threshold. For the MAP/M/c queue with constant impatience times, Choi et al. (Math Oper Res 29:309–325, 2004) derive the virtual waiting time distribution, from which the loss probability and the actual waiting time distribution are obtained. We first refine their result for the virtual waiting time and then derive the stationary queue length distribution. We also discuss the computational procedure for performance measures of interest. Next we consider the stationary M/PH/c queue with constant impatience times and derive the loss probability, the waiting time distribution, and the queue length distribution. Some numerical results are also provided.

Keywords: MAP/M/c queue; M/PH/c queue; Constant impatience time; Loss probability; Waiting time distribution; Queue length distribution; 60K25; 60J25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-015-9455-9

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