An analytic performance model of parallel systems that perform N tasks using P processors that can fail

We present a Markov model for analyzing the performance of parallel/distributed processors that execute a job consisting of N independent tasks in parallel using P processors. The model is a Markov chain with states representing service and failure rates with k (0<k⩽P) active processors. The task-times and processor failures are both exponentially distributed. We derive a number of expressions to determine the mean execution time, probability of success, work, and other measurable quantities, all conditioned on the job finishing successfully. A prototype, implemented using an extended version of ACMPI, is used for actual experiments that are based on simulated task-times and processor failures. We present our results comparing the analytic model with the prototype for a range of values of processor failure rates. We also discuss extensions of the model and issues related to communication costs, approximations and effect of task-time distributions