Response time analysis of repairable multiprocessor systems

In this paper, a simple model to analyze a repairable multiprocessor system using queuing theory is introduced. A closed form solution for the average response time is derived and asserted through simulation. The analysis is done for both homogeneous and heterogeneous multiprocessor systems. Unlike homogeneous systems, processors and/or links speed in heterogeneous systems are not the same. We study the effect of processors speed and links speed on the average response time. We also show how the topology of interconnection network may affect the average response time. Two mechanisms to repair faulty: processors are considered. The immediate repair mechanism gives better average response time than the delayed repair mechanism. An arriving task to a repairable multiprocessor system may not find the number of available processors that give the maximum parallelism and so a minimum response time. Waiting until that number becomes available (repaired) will increase the waiting time. An algorithm is introduced which gives the optimum number of processors that a task must wait before being executed. Waiting for this number will maximize parallelism without excessive increment in waiting time.