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.

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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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