Converging to periodic schedules for cyclic scheduling problems with resources and deadlines

• Published in: Computers & operations research Vol. 51; pp. 227 - 236
• Main Authors: Dupont de Dinechin, Benoît, Munier Kordon, Alix
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.11.2014; Elsevier; Pergamon Press Inc
• Subjects: Applied sciences; Computer Science; Computer science; control theory; systems; Cyclic scheduling; Exact sciences and technology; Inventory control, production control. Distribution; Iterative methods; Language processing and microprogramming; Mathematical problems; Operational research and scientific management; Operational research. Management science; Operations research; Production scheduling; Programming languages; Resource constrained project scheduling problem; Schedules; Scheduling; Scheduling algorithms; Scheduling, sequencing; Software; Software pipelining; Studies; Throughput maximization; Throughput maximization; Resource constrained project scheduling problem; Software pipelining; Cyclic scheduling; Compilation; Out of order processor; Program optimization; Project management; Periodic scheduling; Task analysis; Precedence constraint; Minimum time; List; Delay time; Deadline; Cyclic system; Time lag; Boarded computer; Very long instruction word; Upper bound; Flexible manufacturing system; Resource constraint; Transmission rate; Resource management; Software pipeline; Parallelization
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2014.03.004

Cyclic scheduling has been widely studied because of the importance of applications in manufacturing systems and in computer science. For this class of problems, a finite set of tasks with precedence relations and resource constraints must be executed repetitively while maximizing the throughput. Many applications also require that execution schedules be periodic i.e. the execution of each task is repeated with a fixed global period w. The present paper develops a new method to build periodic schedules with cumulative resource constraints, periodic release dates and deadlines. The main idea is to fix the period w, to unwind the cyclic scheduling problem for some number of iterations, and to add precedence relations so that the minimum time lag between two successive executions of any task equals w. Then, using any usual (not cyclic) scheduling algorithm to compute task starting times for the unwound problem, we prove that either the method converges to a periodic schedule of period w or it fails to compute a schedule. A non-polynomial upper bound on the number of iterations to unwind in order to guarantee that cyclic precedence relations and resource constraints are fulfilled is also provided. This method is successfully applied to a real-life problem, namely the software pipelining of inner loops on an embedded VLIW processor core by using a Graham list scheduling algorithm. •This paper presents a new methodology to build periodic schedules.•Precedence and complex resources constraints are taken into account.•The aim is to minimize the throughput.•Heuristic or exact solution may be obtained.•Our method is successfully applied for executing a vectorial loop on an embedded VLIW processor.