Optimal transmission schedules in TWDM optical passive star networks Original Research Article

This paper is concerned with optimal transmission schedules in the TWDM (time and wavelength division multiplexed) 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 wavelengths (each wavelength is shared by Nk receivers where Nk 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 at any given time slot, at most one transmission can be done per wavelength. An optimal transmission schedule is defined to be the one that schedules transmissions such that for each node v in V, the transmitter in v transmits once to every receiver in V — {v} within a repeating cycle of minimum length. We present an optimal transmission schedule for each tuning time, and show that the cycle length of any optimal transmission schedule is max {N(N — 1)/k, kδ + N — 1}.