Parallel versus Sequential Task-Processing: A New Performance Model in Discrete Time

A main question in parallel computing is the following: Under which conditions should parallel task-processing be preferred to sequential task-processing. In this paper we present stochastic models for the evaluation of the mean time between the creation of a task and the end of its processing. The models are based on the theory of queueing systems in discrete time. We consider closed tandem networks with state-dependent task creation probabilities and bulk arrivals. One of these networks includes a bulk server, another one has state-dependent service completion probabilities approximating the concatenation of a single server station and an inønite server, both with deterministic service times. Analytical and numerical results, which give an answer to the question above, are presented. Keywords: Parallel computing, performance evaluation, queueing networks in discrete time. 1 Introduction Recent research in parallel computing deals with the implementation of algorithms for handling se..