In this paper, we study the delay performance of a circuit switched, self-routing Delta network. A gated hold protocol that retains partial path information is used to guarantee service of all requests. A novel technique that involves the construction of an easier to analyze dominant system is presented. A recursive expression for the probability mass function of the cycle time in the dominant system is derived. Comparison of the dominant system analysis with simulation of the actual system shows that the dominant system accurately predicts performance for low network loads. As network loads increase, the dominant system becomes worse at predicting behavior of the actual system. These results also help develop insight into how to trade off higher delay variability for increased throughput.

The authors analyze a circuit-switched, blocking, multi-stage interconnection network (MIN) with arbitrary independent input distributions and arbitrary switch routing probabilities. The network uses a gated-hold strategy which retains partial path information. By formulating a dominant system, they derive a recursive expression for the mean time to process a batch of requests given a particular input distribution and a set of switch routing probabilities. This system is compared to a simulation of a non-blocking switch implementing a similar gated strategy. Results indicate that this method yields tight bounds for small networks with arbitrary input distributions and switch routing probabilities. For networks with uniform input and output distributions this bound is closer than one introduced in a previous work examining the same protocol.>