A generalized analytic performance model of distributed systems that perform N tasks using p fault-p

Abstract

A family of Markov models for analyzing the performance of parallel processors that execute a job consisting of N independent tasks using P fault-prone processors is presented in this paper. This study extends our previous study by allowing idle processors to fail, and also by developing performance models to analyze the case where one processor is fail-safe. The models are based on Markov Chains with states representing service, and failure rates with k 0 k P active processors. The task-times and processor failures are exponentially distributed. For each performance model we derive a number of expressions to determine the mean execution time, probability of success, standard deviation, work, and the average number of processor failures, all conditioned on the job finishing successfully. We present results of the models for a range of values of processor failure rates. In particular we analyze the results for N = P and N P .