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Invariance in resource-sharing systems

Published online by Cambridge University Press:  14 July 2016

C. Courcoubetis ,
P. Varaiya  and
J. Walrand
C. Courcoubetis*
Affiliation:
University of California, Berkeley
P. Varaiya*
Affiliation:
University of California, Berkeley
J. Walrand*
Affiliation:
University of California, Berkeley
*
∗Present address: Bell Laboratories 7B-212, Murray Hill, NJ 07974, USA.
∗∗Postal address: Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA.
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Abstract

A method for proving the invariance of hitting-time distributions with respect to the control strategy of a Markov chain is presented. The method is applied to resource-sharing problems. It provides a new proof of a known result and extends it. Sufficient conditions for such an invariance are given and are illustrated by examples.

Keywords

HITTING-TIME DISTRIBUTIONSREPAIRMAN PROBLEMRESOURCE ALLOCATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 777 - 785
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported by the Office of Naval Research Contract N00014–80-C-0507.

References

[1] Courcoubetis, C. (1982) Resolving Conflict Among Resource Sharing Processes. Ph.D. Thesis, University of California, Berkeley.Google Scholar
[2] Derman, C, Lieberman, G. U. and Ross, S. M. (1980) On the optimal assignment of servers and a repairman. J. Appl. Prob. 17, 577–581.Google Scholar
[3] Katehakis, M. (1980) Repair of the Service System. Ph.D. Thesis, Columbia University.Google Scholar
[4] Nash, P. and Weber, R. R. (1981) Dominant strategies in stochastic allocation and scheduling problems. In Deterministic and Stochastic Scheduling, ed. Dempster, M. A. H., Lenstra, J. K. and Rinooy Kan, A. H. G. Reidel, Dordrecht.Google Scholar
[5] Smith, D. R. (1978) Optimal repair of the series system. Operat. Res. 26, 653–662.Google Scholar
[6] Weber, R. R. (1980) The Optimal Organization of Multi-service Systems. Ph.D. Thesis, University of Cambridge.Google Scholar