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THE MEAN WAITING TIME FOR A PATTERN

Published online by Cambridge University Press:  01 January 1999

Sheldon M. Ross
Sheldon M. Ross
Affiliation:
Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720
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Abstract

Consider a sequence of independent and identically distributed random variables along with a specified set of k-vectors. We present an expression for E [T], the mean time until the last k observed random variables fall within this set. Not only can this expression often be used to obtain bounds on E[T], it also gives rise to an efficient way of approximating E[T] by a simulation. Specific lower and upper bounds for E[T] are also derived. These latter bounds are given in terms of a parameter, and a Markov chain Monte Carlo approach to approximate this parameter by a simulation is indicated. The results of this paper are illustrated by considering the problem of determining the mean time until a sequence of k-valued random variables has a run of size k that encompasses each value.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 13 , Issue 1 , January 1999 , pp. 1 - 9
Copyright
© 1999 Cambridge University Press

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