PERFORMANCE ANALYSIS OF MULTI-STAGE INTERCONNECTION NETWORKS WITH DETERMINISTIC SERVICE TIMES

Abstract

In this paper we present a performance model for a constant service time, globally synchronized multistage interconnection network that is an improvement on earlier work in this field. The events at the network input are assumed to have a geometric distribution in time. As the events are combined within the network, it can happen that two events arrive simultaneously at one of the network server elements, called a double arrival rate stream (DAR) server. Analytical methods are described to derive the response time and inter-departure time distribution of the double arrival rate constant service time server, which has a queuing property (DAR/D/1). Due to the queuing effect of the servers in the first stage of the network, their outputs show a "distorted" geometric distribution, which is known to introduce analytical difficulties in the performance evaluation of the subsequent stages. A method is presented to derive the response time of servers in the second stage, when the network has a uniform workload distribution. It is shown that the knowledge of the response times of the first and second stage of the network is sufficient to predict the total response time of a large network with an accuracy better than 3%, even under a heavy workload.