Critical Path Scheduling with Resource and Processor Constraints

An investigation is made of the worst-case performance of two related algorithms for scheduling unit-execution-time task systems with resources. Unlike most previous scheduling results for task systems with resources, it is assumed that there are a fixed number of processors in the system. This assumption has both practical and theoretical interest. An upper bound is given for the worst-case performance of critical path scheduling for these task systems. This bound depends on both the number of processors and the number of resources. Moreover, it is shown that this is (asymptotically) the best possible upper bound. It is also noted that exactly the same bound holds for the worst-case performance of Coffman-Graham scheduling. 13 references.