Computation of the distribution of the completion time when the work requirement is a ph random variableThis work was supported in part by the US Office of Naval Research under Contract no. N3014-88-K-0623, by NASA under Grant NAG-1-70, and by the Italian National Research Council CNR under the project “Material and Devices for Solid State Electronics” Grant no. 86.02177.61.

Abstract

In this paper we derive the distribution of the completion time of a job with a PH-distributed work requirement, on a server modeled by a homogeneous Markov reward process. The interactions between the job in progress and the server are allowed to be either of resume or of repeat type in a probabilistic manner. The paper shows that the distribution of the completion time of a job with PH distributed requirement is PH under any mixture of preemptive policies. This result is stated as a closure property of the PH distribution class.

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