On finite exponential moments for branching processes and busy periods for queues
Marvin K. Nakayama, Perwez Shahabuddin, and Karl Sigman
Source: J. Appl. Probab. Volume 41A, Issue
(2004), 273-280.
Abstract
Using a known fact that a Galton-Watson branching process can be
represented as an embedded random walk, together with a result of
Heyde (1964), we first derive finite exponential moment results
for the total number of descendents of an individual. We use this
basic and simple result to prove analogous results for the
population size at time t and the total number of
descendents by time t in an age-dependent branching
process. This has applications in justifying the interchange of
expectation and derivative operators in simulation-based
derivative estimation for generalized semi-Markov processes. Next,
using the result of Heyde (1964), we show that, in a stable
GI/GI/1 queue, the length of a busy period and the number of
customers served in a busy period have finite exponential moments
if and only if the service time does.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1082552204
Digital Object Identifier: doi:10.1239/jap/1082552204
Mathematical Reviews number (MathSciNet): MR2057579
Zentralblatt MATH identifier: 02109925
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