Performance analysis of synchronized iterative algorithms on multiprocessor systems

A statistical model of parallel processing and a performance evaluation technique are introduced. A task is characterized by the number of atoms and by activity. An atom is the smallest part of computation that cannot be distributed to multiple processors and all atoms of a task are assumed to be equal in computational effort. Furthermore, atoms of the task became active with a fixed probability a called the activity. The task is equally divided among processors and the computation is synchronized at periodic instances when the results can be shared. The amount of computational activity of a processor within the period between synchronizations is assumed to be a binomial random variable. The performance of the multiprocessor system is derived from the maximum order-statistic of these random variables. The theoretical performance predicted by the analysis agrees well with the reported experimental performance of logic simulation of production VLSI chips, and several observed phenomena are explainable