Nonpreemptive scheduling of optical switches

Many high-speed routers today use input-queuing (IQ) architectures with a crossbar switching fabric based on optical technology. Packets in the input queues are divided into cells of unit length, and the goal is to find a schedule of minimum makespan that forwards all packets to the output ports. The problem is complicated since, in optical switches, so-called configuration delay, that is the time required to reconfigure the switching fabric, is non-negligible with respect to the cell transmission time. We aim to design a scheduler whose complexity does not depend on the number of packets in the input queues. Thus, we focus on the nonpreemptive bipartite scheduling (NPBS) problem, where each input queue is connected to each output port in at most one configuration. We demonstrate that the NPBS problem is NP-hard for any value of the configuration delay, and approximation within a ratio smaller than 7/6 is NP-hard as well. For the offline version of the NPBS problem, we show that a simple greedy algorithm achieves an approximation factor of 2 for arbitrary configuration delay. Then, we consider the online version of the NPBS problem, where the switch gathers the incoming traffic periodically and then schedules the accumulated batches. We propose a scheduling algorithm that guarantees strict delay for any admissible traffic, provided that the switch has a moderate speed-up of two. Finally, we extend our results to the nonbipartite scheduling problem.