Scheduling jobs on a multiprocessor system with a common memory

Abstract

AbstractThis paper studies the problem of scheduling jobs on a multiprocessor system with a common memory to minimize \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{i = 1}^n {w_i \left({f_i } \right)} $\end{document}, where fi denotes flow‐times of jobs i, and wi(fi) denotes monotonically nondecreasing functions of fi. Arriving jobs are assigned to available processors according to an appropriate scheduling rule. Once a job is placed on a processor, it retains the processor during its processing and repeats local computations and accesses to the common memory. First, the scheduling problem is formulated into a zero‐one integer programming problem. Next, a procedure is presented for computing a lower bound on the optimal cost. Finally, the performance of the proposed procedure is evaluated using simulation experiments for the problem of minimizing mean flow‐time.