A new average case analysis for completion time scheduling

Journal of the ACM

Volumn 53, Issue 1, 2006, Pages 121-146

  Scharbrodt, Mark ^a   Schickinger, Thomas ^a   Steger, Angelika ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b ETH ZURICH   (Switzerland)

Author keywords

Average case analysis; Scheduling theory

Indexed keywords

JOB ANALYSIS; JUST IN TIME PRODUCTION; MATHEMATICAL TECHNIQUES; PROBABILITY DISTRIBUTIONS;

AVERAGE CASE ANALYSIS; EXPONENTIAL DISTRIBUTION; SCHEDULING THEORY;

SCHEDULING;

EID: 33745218250     PISSN: 00045411     EISSN: 00045411     Source Type: Journal    
DOI: 10.1145/1120582.1120585     Document Type: Article

References (35)

1. ABRAMOWTTZ, M., AND STEGUN, I. A., EDS. 1970. Handbook of Mathematical Functions. Dover Publications, New York.
2. ALON, N., AND SPENCER, J. H. 2000. The Probabilistic Method, 2nd ed. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience, New York.
3. BOLLOBÁS, B. 2001. Random Graphs, 2nd ed. Cambridge University Press, Cambridge, MA.
4. BORODIN, A., AND EL-YANIV, R. 1998. Online Computation and Competitive Analysis. Cambridge University Press, Cambridge, MA.
5. BRUNO, J., DOWNEY, P., AND FREDERICKSON, G. N. 1981. Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J. ACM 28, 100-113.
6. BRUNO, JR., E. C., AND SETHI, R. 1974. Scheduling independent tasks to reduce mean finishing time. Commun. ACM 17, 382-387.
7. COFFMAN, JR., E. G., GAREY, M. R., AND JOHNSON, D. S. 1997. Approximation algorithms for bin packing: A survey. In Approximation Algorithms for NP-hard Problems, D. Hochbaum, Ed. 46-93.
8. COFFMANN, JR., E. AND GILBERT, E. N. 1985. Expected relative performance of list scheduling rules. Oper. Res. 33, 548-561.
9. COFFMANN, JR., E. G., SAO, K., HOFRI, M., AND YAO, A. C. 1980. A stochastic model of bin-packing. Inf. Cont. 44, 105-115.
10. CONWAY, R. W., MAXWELL, W. L., AND MILLER, L. W. 1967. Theory of Scheduling. Addison-Wesley, Reading, MA.
11. EASTMAN, W. L., EVEN, S., AND ISAACS, I. M. 1964. Bounds for the optimal scheduling of n jobs on m processors. Manage. Sci. 11, 268-279.
12. GAREY, M. R., AND JOHNSON, D. S. 1998. Computers and Intractability. W. H. Freeman and Company.
13. GRAHAM, R. L., LAWLER, E. L., LENSTRA, J. K., AND RINNOY KAN, A. H. G. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Disc. Math. 5, 287-326.
14. HALL, L. A., SCHULZ, A. S., SHMOYS, D. B., AND WEIN, J. 1997. Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Math. Oper. Res. 22, 513-544.
15. JANSON, S., LUCZAK, T., AND RUCIŃSKI, A. 2000. Random Graphs. Wiley-Interscience, New York.
16. KÄMPKE, T. 1987. On the optimality of static priority policies in stochastic scheduling on parallel machines. J. Appl. Prob. 24, 430-448.
17. KARMAKAR, N. 1982. Probabilistic analysis of some bin-packing algorithms. In Proceedings of the 23rd Annual Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 107-111.
18. KAWAGUCHI, T., AND KYAN, S. 1986. Worst case bound of an LRF schedule for the mean weighted flow-time problem. SIAM J. Comput. 15, 4, 1119-1129.
19. KOUTSOUPIAS, E., AND PAPADIMETRIOU, C. 1994. Beyond competitive analysis. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS '94). IEEE Computer Society Press, Los Alamitos, CA, 394-400.
20. LAGEWEG, B. J., AND LENSTRA, J. K. 1977. manuscript, unpublished. (See Garey and Johnson [ 1998].)
21. MCNAUGHTON, R. 1959. Scheduling with deadlines and loss functions. Manage. Sci. 6, 1-12.
22. MÖHRING, R. H., RADERMACHER, F. J., AND WEISS, G. 1984. Stochastic scheduling problems I: General strategies. Z. Oper. Res. Ser. A. 28, 193-260.
23. MÖHRING, R. H., SCHULZ, A., AND UETZ, M. 1999. Approximation in stochastic scheduling: The power of LP-based priority policies. J. ACM 46, 924-942.
24. PHILLIPS, C., STEIN, C., AND WEIN, J. 1998. Minimizing average completion time in the presence of release dates. Math. Prog. 82, 199-223.
25. PINEDO, M. 1995. Scheduling - Theory, Algorithms, and Systems. Prentice-Hall, Englewood Cliffs, NJ.
26. PORT, S. C. 1994. Theoretical Probability for Applications. Wiley, New York.
27. ROTHKOPF, M. H. 1966. Scheduling with random service times. Manage. Sci. 12, 703-713.
28. SAHNI, S. K. 1976. Algorithms for scheduling independent tasks. J. ACM 23, 116-127.
29. SCHULZ, A. S. 1996. Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds. In Proceedings of the International Conference on Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science, vol. 1084. Springer Verlag, Berlin, Germany, 301-315.
30. SKUTELLA, M. 2001. Convex quadratic and semidefinite programming relaxations in scheduling. J. ACM 48, 206-242.
31. SKUTELLA, M., AND WOEGINGER, G. J. 2000. A PTAS for minimizing the total weighted completion time on identical parallel machines. Math. Oper. Res. 25, 63-75.
32. SMITH, W. E. 1956. Various optimizers for single-stage production. Naval Res. Log. Quatl. 3, 59-66.
33. SOUZA, A., AND STEGER, A. 2006. The expected competitive ratio for weighted completion time scheduling. Theory Comput. Syst., 39, 1 (Feb.), 121-136.
34. WEBER, R. R., VARAIYA, P., AND WALRAND, J. 1986. Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. J. Appl. Prob. 23, 841-847.
35. WEISS, G., AND PINEDO, M. 1980. Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Prob. 17, 187-202.