Optimal transmission schedules in WDM broadcast-and-select networks with multiple transmitters and receivers

In this paper, we study the problem of optimal transmission schedules for embedding complete graphs in WDM broadcast-and-select networks. An optimal transmission schedule is defined to be the one that schedules transmissions such that each node transmits once to every other node within a repeating cycle of minimum length. Our model assumes that the network has N nodes with k wavelength channels, and each node is equipped with multiple tunable transmitters and multiple fixed-tuned receivers. Given /spl alpha/ and /spl beta/ (1/spl les/5/spl alpha/, /spl beta//spl les/k), we first obtain on optimal transmission schedule with schedule length max{/spl alpha//spl beta/N(N-1)/k, /spl beta/(N-1)+k/spl delta/} such that each node transmits to each of its neighboring nodes exactly /spl alpha//spl beta/ times within this time period assuming that each node has a single transmitter and a single receiver. Using this result, we next show that then exists an optimal transmission schedule with average schedule length max{N(N-1)/k, N-1//spl alpha/+k//spl alpha//spl beta/ /spl delta/} when each node has a transmitters and /spl beta/ receivers. We then discuss an O(log k) algorithm to compute optimal numbers of transmitters and receivers to minimize the overall cost of transmitters and receivers in the network while meeting a given bound of schedule length.