Scheduling Techniques for Packet Routing , Load Balancing and Disk

We consider three scheduling problems that arise in studies of packet routing, load balancing and disk scheduling. A fundamental problem in the design of packet-switched communication networks is to provide effective methods for resolving contention when many packets wish to cross a link. End-to-end packet delays should be low and queue sizes should be small. For an adversarial connectionless model we provide upper and lower bounds on delay for many simple algorithms. For an adversarial session-oriented model we prove the existence of an asymptotically optimal schedule with per-packet delay guarantees of O(distance + 1/session rate) and constant queue size. We also describe randomized schedules with near-optimal bounds. In the on-line load balancing problem, jobs arrive on-line and must be assigned to one of a set of machines, thereby increasing the load on that machine by a certain weight. Jobs also depart on-line. The goal is to minimize both the maximum load on a machine and the amount of job reassignment that occurs. For the cases of identical machines and related machines we consider arbitrary reassignment costs and provide the first algorithms that have constant competitive ratios against current load and constant reassignment factors. In the disk scheduling problem we have a set of read and write requests on a computer disk and a convex reachability function that determines how fast the disk head travels between tracks. Our aim is to schedule the head so that it services all the requests in the shortest time possible. Among other things we present a 3/2approximation algorithm (with a constant additive term) for the general case and an optimal polynomial-time solution for the special case in which the reachability function is linear. We also present a heuristic for the on-line problem in which requests arrive over time. Thesis Supervisor: Michel X. Goemans Title: Associate Professor of Applied Mathematics