Transmission schedules for hypercube interconnection in WDM optical passive star networks Original Research Article

This paper is concerned with optimal transmission schedules for a hypercube interconnection using wavelength division multiplexed (WDM) optical passive star network. Our model of the network consists of a set V of N nodes with N tunable transmitters and N fixed-tuned receivers (where each node is assigned a transmitter–receiver pair), k (=2b for an integer b) wavelengths (each wavelength is shared by N/k receivers where N/k is an integer), and tuning time δ>0 (in units of time slot, for transmitters to tune from one wavelength to another). We assume that N is equal to the number of nodes in the hypercube, and that at any given time slot at most one transmission can be done per wavelength. An optimal transmission schedule for a hypercube interconnection is defined to be the one that schedules transmissions such that for each node v of the hypercube, v transmits once to each of its neighboring nodes within a repeating cycle of minimum length. In this paper, we first show that the n-dimensional hypercube Qn can be embedded in V such that for any node of Qn, its n neighboring nodes are evenly partitioned into b groups where each group shares a wavelength. Under this embedding, we then present an optimal transmission schedule for each tuning time.