Local search scheduling algorithms for maximal throughput in packet switches

We consider the (generalized) packet switch scheduling problem, where the switch service configuration has to be dynamically chosen based on observed queue backlogs, so as to maximize the throughput. A class of recently developed ´projective´ scheduling algorithms, which substantially generalize the well-known maximum weight matching (MWM) algorithms for crossbar switches, are explored from the perspective of complexity. The typically huge number of possible switch configurations that the scheduler has to consider in each timeslot has been previously observed to lead to an impractical computational requirement. We introduce a new class of projective schedules based on ´local search´ concepts. In particular, rather than searching the entire (typically huge) set of available service configurations to find the best one, the new scalable scheduling algorithms search ´locally´ over a small neighborhood of service configurations to find a ´better´ one in each time slot. We show that local projective scheduling algorithms can provide dramatic reduction in complexity without causing any loss of throughput (although they may observe higher delay). We explore the nature and structure of such schedules, which show a much higher promise for practical implementation than their global versions.