General Perfectly Periodic Scheduling Extended Abstract

In a perfectly-periodic schedule, time is divided into time-slots, and each client is scheduled precisely every some predefined number of slots, called the period of that client. Periodic sched- ules are useful in wireless communication and other settings. The quality of a schedule is measured by the proportion between the requested and the granted periods: either the maximum over all jobs, or the average. There exist good scheduling algorithms for the average measure in the unit-length single-server model in which all jobs are one slot long, and at most one job is served in each time unit. In this paper we study the general model, where each job may have a different length, and m jobs can be served in parallel for some given m. We give a lower bound for this model which demonstrates the inherent difficulty of multi- ple lengths, and present a sequence of algorithms, culminating in an algorithm for the general case which is asymptotically opti- mal under the maximum ratio measure (and hence also the aver- age ratio measure). The new algorithms utilize new techniques which are rather different from the known algorithms used for the unit-length model. Some of the algorithms improve on the best known bounds for the unit-length model.