Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment

  • Authors:

  • John C. S. Lui;Richard R. Muntz;Don Towsley

  • Affiliations:

  • -;-;-

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1998

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Abstract

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 K 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 驴. Upon the program arrival, it forks into K independent tasks and each task is assigned to an unique server. Each task's service time has a k-stage Erlang distribution with mean service time of 1/驴. 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 (K驴 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.