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<p>The performance of job scheduling is studied in a large parallel processing system where a job is modeled as a concatenation of two stages which must be processed in sequence.P/sub i/ is the number of processors required by stage P as the total number ofprocessors in the system. A large parallel computing system is considered whereMax(/math/). For such systems, exact expressions for the mean system delay are obtained for variousjob models and disciplines. The results show that the priority should be given to jobsworking on the stage which requires fewer processors. The large parallel system condition is then relaxed to obtain the mean system time for two job models whenthe priority is given to the second stage. Moreover, a scale-up rule is introduced toobtain the approximated delay performance when the system provides more processorsthan the maximum number of processors required by both stages. An approximation model is given for jobs with more than two stages.</p>
Index Termsperformance evaluation; dynamic sharing of processors; two-stage parallel processingsystems; job scheduling; mean system delay; mean system time; scale-up rule;approximated delay performance; approximation model; delays; parallel processing;performance evaluation; scheduling

J. Huang and L. Kleinrock, "Performance Evaluation of Dynamic Sharing of Processors in Two-Stage Parallel Processing Systems," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 306-317, 1993.
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