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Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions

  • Gideon Weiss (a1) and Michael Pinedo (a2)
Abstract

We consider preemptive scheduling of N tasks on m processors; processors have different speeds, tasks require amounts of work which are exponentially distributed, with different parameters. The policies of assigning at every moment the task with shortest (longest) expected processing time among those not yet completed to the fastest processor available, second shortest (longest) to the second fastest etc., are examined, and shown to minimize expected values of various cost functions. As special cases we obtain policies which minimize expected flowtime, expected makespan and expected lifetime of a series system with m component locations and N spares.

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Corresponding author
Postal address: Department of Statistics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel.
∗∗ Postal address: Instituto Venezolano de Investigaciones Cientificas (IVIC), Apartado 1827, Caracas 101, Venezuela.
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This work was done while the authors were at the University of California, Berkeley, in the Department of Statistics and the Department of Industrial Engineering and Operations Research, respectively.

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References
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[1] Bruno, J. and Downey, P. (1977) Sequencing tasks with exponential service times on two machines. Technical Report, Department of Computer Sciences, University of California, Santa Barbara.
[2] Frederickson, G. N. (1978) Sequencing tasks with exponential service times to minimize the expected flow time or makespan. Department of Computer Sciences, Pennsylvania State University Report CS–78–07.
[3] Pinedo, M. and Weiss, G. (1979) Scheduling stochastic tasks on two parallel processors. Naval. Res. Logist. Quart. 26, 527535.
[4] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.
[5] Strauch, R. (1966) Negative dynamic programming. Ann. Math. Statist. 37, 871890.
[6] Van Der Heyden, L. (1979) A note on scheduling jobs with exponential processing times on identical processors so as to minimize makespan. Math. Operat. Res.
[7] Weber, R. R. (1979) Scheduling stochastic jobs on parallel machines.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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