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<p><b>Abstract</b>—We study a multiprocessing computer system which accepts parallel programs that have a fork-join computational paradigm. The multiprocessing computer system under study is modeled as <it>K</it> homogeneous servers, each with an infinite capacity queue. Parallel programs arrive at the multiprocessing system according to a series-parallel phase type interarrival process with mean arrival rate of λ. Upon the program arrival, it forks into <it>K</it> independent tasks and each task is assigned to an unique server. Each task's service time has a <it>k</it>-stage Erlang distribution with mean service time of 1/μ. A parallel program is completed upon the completion of its last task. This kind of queuing model has no known closed form solution in the general (<it>K</it>≥ 2) case. In this paper, we show that by carefully modifying the arrival and service distributions at some imbedded points in time, we can obtain tight performance bounds. We also provide a computational efficient algorithm for obtaining upper and lower bounds on the expected response time. The methodology is flexible and allows one to trade-off the tightness of the bounds and computational cost.</p>
High performance computing, performance evaluation, performance modeling methodology, analysis of multiprocessing systems.

D. Towsley, J. C. Lui and R. R. Muntz, "Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment," in IEEE Transactions on Parallel & Distributed Systems, vol. 9, no. , pp. 295-311, 1998.
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