Analysis of the Completion Time of Markov Reward Models

Analysis of Markov Reward Models (MRM) with preemptive resume (prs) policy usually results in a double transform expression, whose solution is based on the inverse transformations both in time and reward variable domain. This paper discusses the case when the reward rates can be either 0 or positive, and analyses the completion time of MRMs. We present a symbolic expression of moments of the completion time, from which a computationally eeective recursive numerical method can be obtained. As a numerical example the mean and the standard deviation of the completion time of a Carnegie-Mellon multiprocessor system are evaluated by the proposed method.