Date: 10 Jun 2005

Some closed form results for circuit switching in a hypercube network

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We consider circuit switching in a hypercube network where each session has to establish a dedicated connection (or circuit) to a destination node for a random length of time. We first obtain an expression for the steady-state probability that a session successfully establishes a circuit, and then obtain analytic expressions for various delay parameters, such as the time between the arrival of a session and the time it is completed (including input queueing delays). The analytic expressions allow the delay parameters to be calculated without performing costly fixed-point iterations, and show how these parameters depend on the session arrival rate and the hypercube dimension.