Critical Path Scheduling of Task Systems with Resource and Processor Constraints

Abstract

Several papers over the past few years have investigated minimum execution time scheduling of unit execution time (UET) task systems with resources. Because such scheduling problems are, in general, NP-hard, a variety of heuristic methods for producing schedules have been studied, among them, critical path scheduling. The strongest results to date have been for systems where there is no processor constraint. These results may be utilized for systems with a processor constraint by treating the processors as an additional resource. Unfortunately, in those cases where the number of processors is close to the number of resources, this results in an upper bound which is somewhat misleading. In this paper we investigate the performance of critical path scheduling for UET task systems with resources and a fixed number of processors. An upper bound for the worst case performance of critical path scheduling is given. This bound depends both on the number of processors and on the number of different resources. Moreover, we show that this is the best possible (asymptotic) upper bound).