Modelling fully-adaptive routing in hypercubes

Analytical models for wormhole-routed hypercubes with deterministic routing have been widely reported in the literature. A model for the hypercube with fully-adaptive routing has recently been proposed in [1]. It uses M/M/1 queues, and computes a different probability of blocking at each intermediate router along the message path. As a result, the number of equations, and thus the computation steps, to evaluate latency increases with the network size. This paper proposes an alternative model that uses M/G/1 queues, and requires a constant number of computation steps irrespective of the network size. It achieves this by computing only once the mean probability of blocking across the entire path, and using it to determine the blocking time at a given router. Simulation experiments reveal that the model yields accurate latency results.