The Nonpreemptive Priority MAP/G/1 Queue

Tetsuya Takine
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Tetsuya Takine: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

Operations Research, 1999, vol. 47, issue 6, 917-927

Abstract: This paper considers the nonpreemptive priority queue with MAP (Markovian Arrival Process) arrivals. Since MAP is weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform.

Keywords: queue; algorithm; algorithmic analysis of a queue with MAP arrivals; queue; priority; nonpreemptive priority; MAP/G/1 queue (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (3)

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