Abstract
Some Real-Time systems may need a multivalence description of tasks. A generic way to achieve it consists in characterizing each task by a Time Value Function (TVF), which gives the contribution of the related task at its actual completion time. This approach can be viewed as a complementary paradigm to the bivalent deadline-driven paradigm, especially in the case of overload. In this paper, we investigate the problem of scheduling a set of TVF-based tasks under the criterion of maximizing the sum of tasks' contributions. To deal with this NP-hard problem, we use a decomposition approach. The latter consists in partitionning the initial task set into several subsets for which we can establish a scheduling order (on the subset level). We propose an algorithm which yields sub-optimal scheduling and finds out the optimal decomposition. This O(n 3) on-line scheduling algorithm yields sequences which are equal or statistically very close to the optimum, as suggested by our simulation study for various scenarii.
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Bagga, P.C., Kalra, K.R. 1980. ‘A Node Elimination Procedure for Towsend's Algorithm for Solving the Single Machine Quadratic Penality Function Scheduling Problem”. Manag. Science, V-26, No. 6, Jun. 1980. pp. 633–636.
Baker, K. R. B., Scudder, G. D.. 1990. ‘Sequencing with earliness and tardiness penalties: a review”, Oper. Res., V.38, No. 1, (Jan.-Feb.). pp. 22–36.
Chen, K.. 1991. ‘A Study on the Timeliness Property in Real-Time Systems”, J. Real-Time Systems, V.3 No.3. pp. 247–273.
Clark R.K.. 1990. “Scheduling Depedent Real-Time Activities’, Ph.D. Thesis, CMU-CS-90-155. Dept. of Computer Science, Carnegie-Mellon University, Aug. 1990.
Coffman Jr. E.G.. 1976. “Computer and Job-Shop Scheduling Theory”. John Wiley & Sons. 1976.
Conway R., Maxwell W., Miller L.. 1967. “Theory of Scheduling”. Addison-Welsey. 1967.
Garey, M. R., Tarjan, R. E., Wilfong, G. T.. 1988. “One-processor scheduling with symmetric earliness and tardiness penalities,” Math. Oper. Res., V 13, No.2, May 1988. pp. 330–348.
Gupta, S. K., Sen, T., 1984. “On The Single Machine Scheduling Problem with Quadratic Penality Function of Completion Times: An Improved Branching procedure,” Manag. Science, V-30, No.5, May. 1984. pp. 644–647.
Held, M., Karp, R.M., 1962. “A Dynamic Programming Approach to Sequencing Problems,” J. SIAM, V 10, No. 1, Mar. 1962. pp. 196–210.
Jensen E.D., Locke C.D., Tokuda H., 1985. “A Time-driven scheduling Model for Real-Time Operating System,” Proc. IEEE Real-Time System Symposium. Dec. 1985. pp. 112–122.
Jensen E.D., 1993. “A Scheduling Model for Scalable Real-Time Computers systems,” Proc. RTS'93, Jan. 93, Paris, France. pp. V.5–V.21.
Knuth D.E., 1969. “The Art of Computer Programming, Volume One: Fundamental Algorithms,” Addison-Welsey, 1969.
Lawler, E. L., Moore, J. M., 1969. “A Functional Equation and its Application to Resource Allocation and Sequencing Problems,”. Manag. Science, V 16, No. 1, Sept. 1969. pp. 77–84.
Le Lann G., 1990. “Critical issues for the development of distributed real-time computing systems.”. INRIA research report, RR-1274, Rocquencourt, France, 1990.
Liu, C.L., Layland, J.W., 1973. “Scheduling Algorithms for Multiprogramming in a hard-real-Time Environment”. J.ACM, V.20, No. 1, Jan. 1973. pp. 46–61.
Locke C.D., 1986. “Best-Effort Decision Making for Real-Time Scheduling,” Ph.D. Thesis, CMU-CS-86-134, Dept. of Computer Science, Carnegie-Mellon University. May, 1986.
Northcutt J.D., 1988. “The Alpha Operating System: Requirements and Rationale,”. Archons Project Tech. Rep. No. 88011, 1988.
Ramamritham, K., Stankovic, J., 1994. “Scheduling Algorithms and Operating systems Support for Real-Time Systems,”. Proc. IEEE, V-82, No. 1, Jan. 1994, pp. 55–67.
Rinooy Kan, A. H. G., 1976. “Machine Scheduling Problems,”. Martinus Nijhoff, the Hague. 1976.
Sahni, S., 1976. “Algorithm for Scheduling Independent Tasks,”. J. ACM, V.23, No. 1, Jan. 1976. pp. 116–127.
Sha, L., Rajkumar, R. Sathaye, S., 1994. “Generalized Rate-Monotonic Scheduling Theory: A Framework for Developing Real-Time Systems,”. Proc. IEEE, V-82, No. 1, Jan. 1994. pp. 68–82.
Shin, K.S., Ramanathan, P., 1994. “Real-Time Computing: A New Discipline of Computer Science and Engineering,”. Proc. IEEE, V-82, No. 1, Jan. 1994. pp. 6–24.
Stankovic, J. A., 1988. “Misconceptions about Real-Time Computing, A Serious Problem for Next-generation Systems,”. IEEE Computer, Oct. 1988. pp. 10–19.
Townsend, W., 1978. “The Single Machine Problem with Quadratic Penality Function of Completion Times: A Branch-and-Bound Solution,”. Manag. Science, V-24, No.5, Jan. 1978. pp. 530–534.
Tokuda H., Wendorf J. W., Wang H.Y., 1987. “Implementation of a Time-driven Scheduler for real-Time operating systems,”. In Proc. IEEE Real-Time Symposium, Dec. 1987. pp. 271–280.
Weiss, H. J., 1981. “A Greedy Heuristic for Single Machine Sequencing with Precedence Constraints,”. Manag. Science, V-27, No. 10, Oct. 1981. pp. 1209–1216.
Wendorf J. W., 1988. “Implementation and Evaluation of a Time-driven Scheduling Processor,” Proc. IEEE Real-Time System Symposium, Dec. 1988. pp. 172–180.
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Chen, K., Muhlethaler, P. A scheduling algorithm for tasks described by Time Value Function. Real-Time Syst 10, 293–312 (1996). https://doi.org/10.1007/BF00383389
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DOI: https://doi.org/10.1007/BF00383389