Trade-offs between speed and processor in hard-deadline scheduling

Abstract

This paper revisits the problem of on-line scheduling of sequential jobs with hard deadlines in a preemptive, multiprocessor setting. An on-line scheduling algorithm is said to be optimal if it can schedule any set of jobs to meet their deadlines whenever it is feasible in the offline sense. It is known that the earliest-deadline-first strategy (EDF) is optimal in a one-processor setting, and there is no optimal on-line algorithm in an mprocessor setting where m 1 2. Recent work (Phihips et al. STOC 971 however reveals that if the on-line algorithm is given faster processors, EDF is actually optimal for all m (e.g., when m = 2, it suffices to use processors 1.5 times as fast). This paper initiates the study of the trade-off between increasing the speed and using more processors in deriving optimal on-line scheduling algorithms. Several upper bound and lower bound results are presented. For example, the speed requirement of EDF can be reduced to2-s when it is given p 2 0 extra processors. The main result is a new on-line algorithm which demands less speedy processors so as to attain optimality (e.g., when m = 2, the speed requirement is 19) and admits a better speed-processor trade-off than EDF (e.g., when m = 2 and p = 1, the speed requirement is 1.2). In Eeneral, no ontimal alnorithm exists when the sneed factor is less than l/(27! 2).