Nearly on Line Scheduling of Preemptive Independent Tasks

Abstract We discuss the problem of scheduling preemptive independent tasks, subject to release dates and due dates, on identical processors, so as to minimize the maximum lateness. This problem was solved by a polynomial flow based algorithm, but the major drawback of this approach is its off-line character. We study a priority algorithm, the equivalent of a list scheduling method in the non-preemptive case, in which tasks are ordered according to their due dates. This algorithm is nearly on-line and of low complexity. It builds an optimal schedule when the release dates are equal. In the general case, it provides an absolute performance guarantee. These results hold when the number of available machines is allowed to vary with time in a zigzag way (the number of machines is either K , or K − 1).

[1]  Zhen Liu,et al.  Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates , 1995, Discret. Appl. Math..

[2]  Günter Schmidt,et al.  Scheduling Independent Tasks with Deadlines on Semi-identical Processors , 1988 .

[3]  E. L. Lawler,et al.  Preemptive Scheduling of. Precedence-Constrained Jobs on Parallel Machines , 1981 .

[4]  Teofilo F. Gonzalez,et al.  A New Algorithm for Preemptive Scheduling of Trees , 1980, JACM.

[5]  W. A. Horn.  Some simple scheduling algorithms , 1974 .

[6]  Eugene L. Lawler,et al.  Preemptive scheduling of uniform machines subject to release dates : (preprint) , 1979 .

[7]  Günter Schmidt,et al.  Scheduling on semi-identical processors , 1984, Z. Oper. Research.

[8]  Edward G. Coffman,et al.  Preemptive Scheduling of Real-Time Tasks on Multiprocessor Systems , 1970, JACM.

[9]  Jeffrey D. Ullman,et al.  NP-Complete Scheduling Problems , 1975, J. Comput. Syst. Sci..

[10]  Danny Dolev,et al.  Scheduling Flat Graphs , 1985, SIAM J. Comput..

[11]  Robert McNaughton,et al.  Scheduling with Deadlines and Loss Functions , 1959 .

[12]  Sartaj Sahni,et al.  Preemptive Scheduling with Due Dates , 1979, Oper. Res..

[13]  Jacques Carlier,et al.  Scheduling jobs with release dates and tails on identical machines to minimize the makespan , 1987 .

[14]  Kevin Mahon,et al.  Deterministic and Stochastic Scheduling , 1983 .

[15]  Manfred K. Warmuth,et al.  Profile Scheduling of Opposing Forests and Level Orders , 1985 .

[16]  Éric Sanlaville.  Conception et analyse d'algorithmes de liste en ordonnancement preemptif , 1992 .