Abstract
A closed single‐server system is considered in which n items are scheduled to circulateat a fixed period. Each service is recognizable and is scheduled for its individual point of time;it is non‐preemptive and its length depends only on which item is being served.Aberratingfrom this desired schedule, some of the items start out with delays. While an item isdelayed,the time between a departure it makes from the server and its next arrival at the server isshortened by an item‐specific parameter. The aim is to recover the regular schedule asearlyas possible, or minimizing the sum of delays on services. All services must be executedeven if delayed.A greedy algorithm for a tractable subproblem is given. The overall problem is proved Σ2-hard; some subproblems are proved NP-hard. For one ofthe latter, an approximationalgorithm is given whose performance ratio approaches one if the maximum delay is largeenough relative to other parameters. It is proved that without this natural restriction,therecan be no algorithm with asymptotic performance ratio one.
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References
J.A. Bannister and K.S. Trivedi, Task allocation in fault-tolerant distributed systems, Acta Informatica 20(1983)261-281.
S.K. Baruah, L.E. Rosier, I. Tulchinsky and D. Varvel, The complexity of periodic maintenance, in: Proc. International Computer Symposium, Hsinchu, Taiwan, 1990.
S.K. Baruah, R.R. Howell and L.E. Rosier, On preemptive scheduling of periodic, real-time tasks on one processor, MFCS(1990)173-179.
M.Y. Chan and F.Y.L. Chin, General schedulers for the pinwheel problem based on double-integer reduction, IEEE Trans. Comp. 41(1992)755-768.
T. Cormen, C. Leiserson and R. Rivest, An Introduction to Algorithms, The MIT Press/McGraw-Hill, New York, 1990.
M.R. Garey and D.S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
C.-C. Han and K.-J. Lin, Scheduling real-time computations with separation constraints, IPL 42(1992)61-66.
R. Holte, L. Rosier, I. Tulchinsky and D. Varvel, Pinwheel scheduling with two distinct numbers, TCS 100(1992)105-135.
C. Hurkens, Large scale periodic scheduling, Talk presented at the 3rd Workshop on Models and Algorithms for Planning and Scheduling Problems, Cambridge, UK, 1997.
V.B. Kats, An exact optimal cyclic scheduling algorithm for multioperator service of a production line, Automation and Remote Control 43(1982)538-542.
J. Korst, Periodic Multiprocessor Scheduling, Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1992.
C.M. Krishna and K.G. Shin, On scheduling tasks with a quick recovery from failure, IEEE Trans. Comput. 35(1986)448-455.
C.L. Liu and J.W. Layland, Scheduling algorithms for multiprogramming in a hard-real-time environment, J. ACM 20(1973)46-61.
N.V.R. Mahadev, Ph. Solot and D. de Werra, The cyclic compact open-shop scheduling problem, Discr. Math. 111(1993)361-366.
A. Mok, L.E. Rosier, I. Tulchinsky and D. Varvel, Algorithms and complexity of the periodic maintenance problem, Microprocessing and Microprogr. 27(1989)657-664.
R. Roundy, Cyclic schedules for job shops with identical jobs, M. of OR 17(1992) 842-865.
P. Serafini and W. Ukovich, A mathematical model for periodic scheduling problems, SIAM J. Discr. Math. 2(1989)550-581.
P. Serafini, G. Lancia and F. Rinaldi, Improving algorithms for periodic scheduling, Talk presented at the 3rd Workshop on Models and Algorithms for Planning and Scheduling Problems, Cambridge, UK, 1997.
E.D. Tempero and R.E. Ladner, R.E., Recoverable sequence transmission protocols, J. ACM 42(1995)1059-1090.
A. Vince, Scheduling periodic events, Discrete Applied Mathematics 25(1989)299-310.
R. Wegner, Recovering cyclic schedules from delay, Research Report, University of Dortmund, 1996/1998; http://ls2-www.informatik.uni-dortmund.de/wegner/
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Wegner, R. Recovering cyclic schedules from delay. Annals of Operations Research 92, 143–164 (1999). https://doi.org/10.1023/A:1018978529821
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DOI: https://doi.org/10.1023/A:1018978529821