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The Nonpreemptive Priority MAP/G/1 Queue

Author

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  • Tetsuya Takine

    (Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan)

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.

Suggested Citation

  • Tetsuya Takine, 1999. "The Nonpreemptive Priority MAP/G/1 Queue," Operations Research, INFORMS, vol. 47(6), pages 917-927, December.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:6:p:917-927
    DOI: 10.1287/opre.47.6.917
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    References listed on IDEAS

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    1. Gagan L. Choudhury & David M. Lucantoni, 1996. "Numerical Computation of the Moments of a Probability Distribution from its Transform," Operations Research, INFORMS, vol. 44(2), pages 368-381, April.
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    Cited by:

    1. Attahiru Sule Alfa & Bin Liu & Qi‐Ming He, 2003. "Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 662-682, September.
    2. Joris Walraevens & Thomas Giel & Stijn Vuyst & Sabine Wittevrongel, 2022. "Asymptotics of waiting time distributions in the accumulating priority queue," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 221-244, August.
    3. Sofian De Clercq & Joris Walraevens, 2020. "Delay analysis of a two-class priority queue with external arrivals and correlated arrivals from another node," Annals of Operations Research, Springer, vol. 293(1), pages 57-72, October.

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