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 α and β (1⩽5α, β⩽k), we first obtain on optimal transmission schedule with schedule length max{αβN(N-1)/k, β(N-1)+kδ} such that each node transmits to each of its neighboring nodes exactly αβ 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/α+k/αβ δ} when each node has a transmitters and β 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