The Power of Migration in Multi-Processor Scheduling of Real-Time Systems

In this paper we study the performance of off-line multiprocessor real-time schedules that allow task migration compared to those that forbid migration. We consider an off-line scheduling problem in which a given collection of tasks, each with a release time, computation time, and deadline, are to be run on a multiprocessor system. A preemptive schedule allows the execution of a task to be temporarily suspended and resumed at a later time. A migrative schedule allows the task to resume on any processor whereas a nonmigrative schedule allows the task to resume only on the processor in which it was initially started. A schedule value is the summation of all the values of all the tasks that were completed by their deadlines. In this paper we assume that a task's value is proportional to its computation time. We present lower and upper bound results. For a system with n processors, we construct a nonmigrative schedule that is guaranteed to achieve at least $1-( 1-\frac 1{2n}) ^n$ of the optimal migrative schedule value. In addition, we show task sets for which even an optimal nonmigrative schedule achieves at most n/(2n-1) of the optimal migrative value. Asymptotically (as $n\rightarrow \infty $) our upper bound approaches 1/2 and the lower bound approaches $1 - {1\over \sqrt{e}} \sim 0.3935$.