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Aspects of Lagrangian probability distributions

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Masaaki Sibuya ,
Norihiko Miyawaki  and
Ushio Sumita
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Abstract

Lagrangian distributions are reviewed from the viewpoint of the Galton-Watson process. They are related to the busy period in queuing systems and to the first visit in random walks.

A property of the distributions is remarked for the application to vacant vehicles in a new transit system. Combinatorial identities of multinomial and binomial coefficients and related recurrences are shown by a probabilistic method. Based on the identities and recurrences, random forests generated by the Poisson and geometric Galton-Watson processes are characterized.

Keywords

BUSY PERIODCOMBINATORIAL IDENTITYFIRST VISITRANDOM FORESTGALTON-WATSON PROCESSPRIORITY QUEUE

MSC classification

Primary: 60E05: Distributions
Secondary: 60K25: Queueing theory
Type
Part 3 Queueing Theory
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 185 - 197
Copyright
Copyright © Applied Probability Trust 1994 

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