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An enumerative approach to a problem in probability

Published online by Cambridge University Press:  14 July 2016

John S. Devitt
John S. Devitt*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
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Abstract

Sequences over the finite alphabet {1, …, m} are used to model the various job queues of a machine, classifying each job according to which one of a set of m resources is used by the job. Known results concerning the enumeration of such sequences according to the number of rises, levels and falls are then used to obtain the various moments of the distribution of the random variable for the number of changes of resources occurring in a sequence of n jobs given the conditional probabilities of changing resources between independent jobs. The techniques involved form a useful approach to problems where such enumerative information is available.

Keywords

SEQUENCE MODELSSEQUENCE ENUMERATIONJOB QUEUESGENERATING FUNCTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 129 - 137
Copyright
Copyright © Applied Probability Trust 1979 

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References

Jackson, D. M. (1977) The unification of certain enumeration problems for sequences. J. Combinatorial Theory A 22, 92–96.Google Scholar
Kaplan, W. (1973) Advanced Calculus. Addison Wesley, Don Mills, Ont.Google Scholar
Liu, C. L. (1968) Introduction to Combinatorial Mathematics. McGraw-Hill, New York.Google Scholar
Tutte, W. T. (1975) On elementary calculus and the Good formula. J. Combinatorial Theory B 18, 97–137.Google Scholar