Traffic Studies of Unbuffered Delta Networks

This paper analyzes the performance of unbuffered Delta networks under a nonuniform (“hot-spot”) traffic pattern. Particular attention is paid to characterizing the overflow traffic of unsuccessfully transmitted packets. Analytic techniques are used to show that the overflow traffic from an unbuffered packet-switched Delta network is (fractionally) hotter than the offered load. Simulation techniques are used to extend this result to an unbuffered circuitswitched network with limited retrials. In addition, the distribution of the number of trials until a “cold” packet is successfully delivered is shown to have a decreasing hazard rate, which means that it becomes less and less likely with each successive trial that a packet is delivered successfully. The implications of these results for hierarchical networks, a class of networks for interconnecting a highly parallel, sharedmemory multiprocessor computer system, are discussed.