Performance analysis of parallel processing systems

Abstract

A centralized parallel processing system with job splitting is considered. In such a system, jobs wait in a central queue, which is accessible by all the processors, and are split into independent tasks that can be executed on separate processors. This parallel processing system is modeled as a bulk arrival MX/M/c queueing system where customers and bulks correspond to tasks and jobs, respectively. Such a system has been studied in [1, 3] and an expression for the mean response time of a random customer is obtained. However, since we are interested in the time that a job spends in the system, including synchronization delay, we must evaluate the bulk response time rather than simply the customer response time. The job response time is the sum of the job waiting time and the job service time. By analyzing the bulk queueing system we obtain an expression for the mean job waiting time. The mean job service time is given by a set of recurrence equations.

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