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SOME RESULTS FOR SKIP-FREE RANDOM WALK

Published online by Cambridge University Press:  19 August 2010

Mark Brown,
Erol A. Peköz and
Sheldon M. Ross
Mark Brown
Affiliation:
Department of Mathematics, City College, CUNY, New York, NY E-mail: cybergarf@aol.com
Erol A. Peköz
Affiliation:
School of Management, Boston University, Boston, MA 02215, E-mail: pekoz@bu.edu
Sheldon M. Ross
Affiliation:
Department of Industrial and System Engineering, University of Southern California, Los Angeles, CA 90089, E-mail: smross@usc.edu
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Abstract

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A random walk that is skip-free to the left can only move down one level at a time but can skip up several levels. Such random walk features prominently in many places in applied probability including queuing theory and the theory of branching processes. This article exploits the special structure in this class of random walk to obtain a number of simplified derivations for results that are much more difficult in general cases. Although some of the results in this article have appeared elsewhere, our proof approach is different.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 4 , October 2010, pp. 491 - 507
Copyright
Copyright © Cambridge University Press 2010

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