On Traffic Allocations in Optical Packet Switches

In this paper, we study the impacts of traffic allocations on the performance of optical packet switches (OPS). In particular, two different cases are investigated where traffic loads are distributed over different (i) time slots (time dimension); and (ii) output ports (space dimension), respectively. These two cases are of significant importance as each has different applications and they form the basis of some more complicated schemes. Our main contributions are three fold. Firstly, for the most fundamental OPS configuration, we prove that its packet loss is a convex function of traffic load. For any other node configuration, we prove that its packet loss remains as a convex function of traffic load as long as a simple condition is satisfied. Secondly, for any OPS with its packet loss as a convex function of traffic load, we propose a simple algorithm for efficiently comparing some different traffic-allocations and telling which one of them leads to the lowest packet loss. We also show that in either time or space dimension, the best packet-loss performance is achieved when traffic loads are uniformly distributed. Thirdly, for OPS with limited capability of adjusting a given traffic distribution, we propose a Load Balancing (LB) algorithm to minimize the packet loss. These contributions provide some useful guidelines and algorithms for achieving efficient traffic allocations in various OPS networks.