ABST~tACT. In multiprogramming computer systems, the scheduling strategy used to select tasks to be activated is an important factor in the achievement of the performance goals of the system. One form of analysm of scheduling algorithms represents the system as an abstract model of computation and then formally analyzes the algorithms operating in the context of the model. This paper presents an abstract system model which consists of several identical and independent task processors and a memory of arbitrary size Tasks are represented by processing-time and memory requirements which must be met by the model. Worst-case performance bounds are derived for sever al simple scheduling algortthms. A new heuristic algorithm, which uses a look-ahead strategy, is introduced This algorithm is shown to be better in many cases than the simpler algorithms when the worst-case performance bounds are compared.KEY WORnS ANn PHRASES: multiprogram ruing computer system, task scheduling, scheduling algorithms, deterministic scheduling models, worst-csse performance bounds ca CATEGORIES: 4.32, 5.39

of the Los Alamos Scientific Laboratory, has discovered several errors in this paper. Although most of these were of a minor nature, he did discover a significant flaw m the proof of case 4, Theorem 4.5. The authors have dtscovered a vahd proof for case 4; unfortunately, the proof of case 7, Theorem 4.5, depended on the incorrect proof of case 4. A valid proof for case 7 has not yet emerged A bound for case 7 which has been proved is the general bound of 3 -3In from Theorem 3.1. The authors have not discovered a counterexample for case 7 and do conjecture that it remains vahd Complete errata correcting all known errors are avadable by contacting the authors at

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This paper presents a description and analysis of a task scheduling algorithm which is applicable to third generation computer systems. The analysis is carried out using a model of a computer system having several identical task processors and a fixed amount of memory. The algorithm schedules tasks having different processor-time and memory requirements. The goal of the algorithm is to produce a task schedule which is near optimal in terms of the time required to process all of the tasks. An upper bound on the length of this schedule is the result of deterministic analysis of the algorithm. Computer simulations demonstrate the applicability of the algorithm in actual systems, even when some of the basic assumptions are violated.