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Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue

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  • Attahiru Sule Alfa
  • Bin Liu
  • Qi‐Ming He

Abstract

We use the matrix‐geometric method to study the MAP/PH/1 general preemptive priority queue with a multiple class of jobs. A procedure for obtaining the block matrices representing the transition matrix P is presented. We show that the special upper triangular structure of the matrix R obtained by Miller [Computation of steady‐state probabilities for M/M/1 priority queues, Oper Res 29(5) (1981), 945–958] can be extended to an upper triangular block structure. Moreover, the subblock matrices of matrix R also have such a structure. With this special structure, we develop a procedure to compute the matrix R. After obtaining the stationary distribution of the system, we study two primary performance indices, namely, the distributions of the number of jobs of each type in the system and their waiting times. Although most of our analysis is carried out for the case of K = 3, the developed approach is general enough to study the other cases (K ≥ 4). © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 662–682, 2003.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:6:p:662-682
    DOI: 10.1002/nav.10083
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    References listed on IDEAS

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    1. Douglas R. Miller, 1981. "Computation of Steady-State Probabilities for M / M /1 Priority Queues," Operations Research, INFORMS, vol. 29(5), pages 945-958, October.
    2. 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.
    3. Tetsuya Takine, 1999. "The Nonpreemptive Priority MAP/G/1 Queue," Operations Research, INFORMS, vol. 47(6), pages 917-927, December.
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    1. 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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