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A performance evaluation of a general parallel processing model

1990

Abstract

In this paper we analyze a model of a parallel processing syslem. In our model there is a single queue which is scrvcd by K 1 1 identical proccs-SOTS. Jobs arc assumed LO consist of a scqucnce of barrier synchronizations where, at each step, the number of tasks that must be synchronixcd is random with a known distribution. An exact analysis of the model is dcrivcd. The model lcads to a rich set of rcsul(x characterizing the performance of parallel processing syslcms. WC show Ihal, the number of jobs concurrenlly in execution, as well as I.hc number 0C synchronixation varia.bles, grows linearly wi1.h Ihe load or the system and strongly dcpcntls on the avcragc number of parallel lasks Found in the workload. I'ropcrtics of expected rcsponsc I,imc or such syslcms arc exbcnsively analyzed and, in parliciilar, wc report on some non-obvious response time behavior that arises as a function of l;hc variance of parallelism round in the work1oa.d. Rascd on exact response lime analysis, we propose a simple calculalion lhat can be used as a rule of t.humh 1.0 predict speedups. This can be viewed a.s a gcncra.lizalion of Amdahl's law t.hat includes qucucirrg cC fccts. This gcncralizat.ion. is rcformulalcd when prccisc workloads cannot be characterizccl, but raohcr when only Ihc fraclion or scquerrtial work and the average number or parallcl tasks arc assumcd to bc known.