A universal analytic model for photonic Banyan networks

One of the important considerations in designing waveguide-based photonic switching networks is to avoid crosstalk. Two approaches have been proposed which dilate a network in the space and time domains, respectively, to establish crosstalk-free connections. The space-domain dilation uses more hardware, representing cost in space, while the time-domain dilation uses more rounds (or time slots), representing cost in time. In order to evaluate the space-time tradeoffs involved in these two approaches, an analytical model is developed. We describe a recursive procedure which calculates the probability that a new connection can be established without crosstalk in a Banyan (or dilated Banyan) network by taking into consideration the dependency between traffic distributions at different stages. A Markov process based on such probabilities is then used to determine the average number of rounds needed for a set of one-to-one random connections. The model is applicable to both Banyan and dilated Banyan networks, with either stage or individual control. Simulation results are also obtained and compared to the analytic results. We show that the time-domain approach can achieve better space-time tradeoffs than the space-domain approach. One of the practical implications of this result is that a multiplane Banyan network may be more cost-effective than a dilated Banyan in avoiding crosstalk.