Scheduling tasks with ready times and deadlines to minimize average error

• Authors: W. Shih;J. S. W. Liu;J. Chung;D. W. Gillies
• Venue: ACM SIGOPS Operating Systems Review
• Year: 1989

We consider here the problem of scheduling tasks each of which islogically decomposed into a mandatory subtask and an optionalsubtask. The mandatory subtask must be executed to completion inorder to produce an acceptable result. The optional subtask beginsafter the mandatory subtask is completed and refines the result inorder to reduce the error in the result. If the available processortime is insufficient, the optional subtask can be left incompleted.The error in the result of a task is equal to the processing timeof the unexecuted portion of the optional subtask. We describe apreemptive algorithm for scheduling n dependenttasks with rational ready times, deadlines, and processing times onuniprocessor systems. This algorithm is optimal in the sense thatit finds feasible schedules meeting ready-time and deadlineconstraints of all tasks and minimizing the average error of alltasks, whenever feasible schedules exist. The complexity of thisalgorithm isO(n2log2n).This algorithm can also be used to schedule optimally independenttasks with rational ready times, deadlines and processing times onidentical multiprocessor systems. R@Liu, J. W. S., K. J.Lin, and S. Natarajan, "Scheduling real-time, periodic jobs usingimprecise results," Proceedings of the IEEE 8th Real-TimeSystems Symposium, San Jose, California, December 1987.RChung, J. Y. and J. W. S. Liu, "Performance of algorithmsfor scheduling periodic jobs to minimize average error,"Proceedings of the IEEE 9th Real-Time SystemsSymposium, Huntsville, Alabama, December 1988.RChung, J. Y. and J. W. S. Liu, "Performance of algorithmsfor scheduling periodic jobs to avoid timing faults," to appear inthe Proceedings of 22nd Hawaii International Conference onSystem Sciences, Hawaii, 1989. RLin, K. J., S.Natarajan, J. W. -S. Liu, and T. Krauskopf, "Concord: a system ofimprecise computations," Proceedings of the 1987 IEEECompsac, Japan, October, 1987. RBlazewicz, J.and G. Finke, "Minimizing mean weighted execution time loss onidentical and uniform processors", Information ProcessingLetters, Vol. 24, pp. 259--263, March 1987.RChong, E. K. P. and W. Zhao, Performanceevaluation of scheduling algorithms for imprecise computersystems, Technical Report, Department of ComputerScience, University of Adelaide, SA 5001, Australia, September1988. RChong, E. K. P. and W. Zhao, Usercontrolled optimization in task scheduling for imprecise computersystems, Technical Report, Department of ComputerScience, University of Adelaide, SA 5001, Australia, October 1988.RLawler, E. L. and J. M. Moore, "A functional equation andits application to resource allocation and scheduling problem,"Management Science, Vol. 16, pp. 77--84, 1969.RMcNaughton, R., "Scheduling with deadlines and lossfunctions," Management Science, Vol. 12, pp.1--12, 1959. RTarjan, R. E., Data Structures andNetwork Algorithms, Society for Industrial and AppliedMathematics, Pennsylvania, 1983. RShih, W. K., J. W. S.Liu, J. Y. Chung, and D. W. Gillies, Scheduling tasks withready times and deadlines to minimize average error,Technical Report, Department of Computer Science, University ofIllinois, January 1989.