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 allows task migration compared to those that forbid migration. We consider an off-line scheduling problem in which a given collection of tasks each with release time, computation time and deadline are to be run on a multi-processor 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 the non-migrative schedule allows the task to resume only on the processor 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 value is proportional to its computation time. We present lower and upper bound results. For a system with n processors, We construct a non-migrative schedule that achieves a fraction of at least 1-(1-1/2n)ⁿ of the optimal migrative schedule value. In addition, we construct task sets, for which even an optimal non-migrative schedule achieves at most n/(2n-1) of the optimal migrative value. Notice, that asymptotically (as n→∞) our upper bound approaches 1/2 and the lower bound approaches 1-1/√e to approximately 0.3935.