Scheduling on two Uniform Processors with Resource Constraints to Minimize Mean Flow Time

Abstract

In this paper, we study the problem of scheduling a set of tasks to minimize mean flow time. The tasks have equal processing time and are scheduled on two uniform processors. The faster processor is b times faster than the slower one. The schedule needs to satisfy the resource constraints, that is, there are r units of resources, all are of the same kind. At any instant, the total number of resources held by the tasks executed on both uniform processors is less than or equal to r. Tasks are not preemptive. We propose an O(n2) algorithm to find an asymptotically optimal schedule for this problem. Our algorithm can be extended to develop a good approximation algorithm for a multiprocessor system with arbitrary number of processors.