Performance/Reliability Modeling for Multi-Processor Systems with Computational Demands

Abstract

A multi-processor system can attain high reliability and performance simultaneously. Several measures featuring the reliability or the performance have been proposed independently. However, these measures cannot feature the reliability and performance simultaneously. In this paper we propose a few measures featuring the reliability and performance simultaneously, which are the expected numbers of lost jobs by the failure and by the cancellation, and so on. We discuss a multi-processor system with a buffer, in which each processor and buffer can fail, and be repaired independently. Assuming that the failure time is exponentially distributed and the repair time is arbitrarily distributed, and introducing the coverage, we analyze such a generalized model. Applying Markov renewal processes and queueing theory, we derive some important measures numerically. Numerical examples show several measures. In particular, the following measures are of great Interest; the expected number of lost jobs by the cancellation which should be minimized, and the expected system throughput which should be maximized. Such measures give an optimum storage capacity of the buffer balancing the tradeoffs between performance and reliability.