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Matrix‐geometric solution of discrete time MAP/PH/1 priority queue
Author(s) -
Alfa Attahiru Sule
Publication year - 1998
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(199802)45:1<23::aid-nav2>3.0.co;2-n
Subject(s) - priority inheritance , queue , matrix (chemical analysis) , priority queue , computer science , class (philosophy) , mathematical optimization , mathematics , computer network , dynamic priority scheduling , artificial intelligence , materials science , composite material , quality of service , rate monotonic scheduling
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