On the Performance of Synchronized Programs in Distributed Networks with Random Processing Times and Transmission Delays

A synchronizer is a compiler that transforms a program designed to run in a synchronous network into a program that runs in an asynchronous network. The behavior of a simple synchronizer, which also represents a basic mechanism for distributed computing and for the analysis of marked graphs, was studied in ER1] and ER2] under the assumption that message transmission delays and processing times are constant. In this paper we study the behavior of the simple synchronizer when processing times and transmission delays are random. Our main performance measure is the rate of a network, i.e., the average number of computational steps executed by a processor in the network, per unit time. We analyze the eeect of the topology and the probability distributions of the random variables on the behavior of the network. For random variables with exponential distribution we provide tight (i.e. attainable) bounds and study the eeect of a bottleneck processor on the rate.