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

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

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Article ID: iaor20042349
Country: United States
Volume: 50
Issue: 9
Start Page Number: 662
End Page Number: 682
Publication Date: Sep 2003
Journal: Naval Research Logistics
Authors: , ,
Keywords: M/M/1 queues, M/G/1 queues
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 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 K = 3, the developed approach is general enough to study the other cases (K ≥ 4).

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