Abstract

The talk reviews the history and recent results on the scheduling of tasks that require access to a set of resources. The first step was the discovery that maximum weighted matching achieves the maximum throughput for a class of such scheduling problems that includes wireless networks and packet switches. However, this algorithm is too complex to be directly applicable. The second step was understanding when a simpler algorithm, longest queue first, also achieves maximum throughput. The third step was inventing a distributed algorithm where tasks select an independent random back off delay before asking for the resources; this delay has a mean value that decreases exponentially with the backlog. Using stochastic approximation theory, one shows that this algorithm achieves the maximum throughput. The fourth step is a modification of maximum weight matching to achieve the maximum utility in a processing network where tasks not only share resources but also require access to parts. The talk explains the intuition behind the results and the main ideas of the proofs.