A UNIVERSAL ANALYTIC MODEL FOR PHOTONIC BANYAN NETWORKS

One of the important considerations in designing waveguide-based photo nic switching networks is to avoid crosstalk, Two approaches have been proposed which dilate a network in the space and time domains, respec tively, to establish crosstalk-free connections. The space-domain dila tion uses more hardware, representing cost in space, while the time-do main dilation uses more rounds (or time slots), representing cost in t ime. In order to evaluate the space-time tradeoffs involved in these t wo approaches, an analytical model is developed. We describe a recursi ve procedure which calculates the probability that a new connection ca n be established without crosstalk in a Banyan (or dilated Banyan) net work by faking into consideration the dependency between traffic distr ibutions at different stages. A Markov process based on such probabili ties 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 bo th Banyan and dilated Banyan networks, with either stage or individual control. Simulation results are also obtained and compared to the ana lytic results, me show that the time-domain approach can achieve bette r space-time tradeoffs than the space-domain approach. One of the prac tical implications of this result is that a multiplane Banyan network may be more cost-effective than a dilated Banyan in avoiding crosstalk .