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Matrix‐geometric solution of discrete time MAP/PH/1 priority queue

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  • Attahiru Sule Alfa

Abstract

We use the matrix‐geometric method to study the discrete time MAP/PH/1 priority queue with two types of jobs. Both preemptive and non‐preemptive cases are considered. We show that the structure of the R matrix obtained by Miller for the Birth‐Death system can be extended to our Quasi‐Birth‐Death case. For both preemptive and non‐preemptive cases the distributions of the number of jobs of each type in the system are obtained and their waiting times are obtained for the non‐preemptive. For the preemptive case we obtain the waiting time distribution for the high priority job and the distribution of the lower priority job's wait before it becomes the leading job of its priority class. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 23–50, 1998

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  • Attahiru Sule Alfa, 1998. "Matrix‐geometric solution of discrete time MAP/PH/1 priority queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 23-50, February.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:1:p:23-50
    DOI: 10.1002/(SICI)1520-6750(199802)45:13.0.CO;2-N
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    References listed on IDEAS

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    1. Edward P. C. Kao & Kumar S. Narayanan, 1990. "Computing Steady-State Probabilities of a Nonpreemptive Priority Multiserver Queue," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 211-218, August.
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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.

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