Comparison of task response times in parallel systems

Generic queuing models of parallel systems with K ≥ 2 exponential servers, where jobs may be split into K independent tasks, are considered. The queuing of jobs is distributed if each server has its own queue and centralized if there is a common queue. The scheduling of jobs is no splitting if all tasks of a job must run on one processor and splitting if they can run concurrently on different processors. Exact and approximate expressions for the mean response time, Tr, of the rth, r = 1, 2, ..., K, departing task in a job are obtained and compared for four models: distributed/spitting, distributed/no splitting, centralized/splitting, and centralized/no splitting. The queuing models are described. Exact and approximate analyses of the various models are presented where expressions are obtained for the mean task response time. The various models are compared and applications in the areas of distributed query processing and parallel systems are included.