Scheduling light-trails on WDM rings

We consider the problem of scheduling communication on optical WDM (wavelength division multiplexing) networks using the light-trails technology. We give two online algorithms which we prove to have competitive ratios O(log n) and O(log n) respectively. We also consider a simplification of the problem in which the communication pattern is fixed and known before hand, for which we give a solution using O(c + log n) wavelengths, where c is the congestion and a lower bound on the number of wavelengths needed. While congestion bounds are common in communication scheduling, and we use them in this work, it turns out that in some cases they are quite weak. We present a communication pattern for which the congestion bound is O(log n/ log log n) factor worse than the best lower bound. In some sense this pattern shows the distinguishing character of light-trail scheduling. Finally we present simulations of our online algorithms under various loads.