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Analysis of the Completion Time of Markov Reward Models and its Application
Miklós Telek, András Pfening, Gábor Fodor 3
Abstract
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 effective 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.
Key words: Markov Reward Models, Preemptive Resume Policy, Completion Time.
Footnotes:
1 A. Pfening and M. Telek thank Hungarian OTKA for grant No. F-23971.
2 A. Pfening and M. Telek thank Hungarian OTKA for grant No. F-23971.
3 Department of Telecommunications and Telematics, Technical University of Budapest, P.O.B. 91, 1521 Budapest, Hungary