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An approximation of stopped sums with applications in queueing theory

Published online by Cambridge University Press:  01 July 2016

Miklós Csörgő ,
Paul Deheuvels  and
Lajos Horváth
Miklós Csörgő*
Affiliation:
Carleton University
Paul Deheuvels*
Affiliation:
Université Paris VI
Lajos Horváth*
Affiliation:
Szeged University
*
∗Postal address: Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
∗∗ Postal address: Université Paris VI, t.45–55, E3, L.S.T.A., 4 Place Jussieu, 75230 Paris Cedex 05, France.
∗∗∗ Postal address: Bolyai Institute, Szeged University, H-6720 Szeged, Aradi vértanúk tere 1, Hungary.
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Abstract

We prove strong approximations for partial sums indexed by a renewal process. The obtained results are optimal. The established probability inequalities are also used to get bounds for the rate of convergence of some limit theorems in queueing theory.

Keywords

STOPPED SUMSWIENER PROCESSRENEWAL PROCESSGI/G/1 QUEUEKINGMAN&S HEAVY TRAFFIC APPROXIMATION
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 3 , September 1987 , pp. 674 - 690
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported by an NSERC Canada grant at Carleton University.

Research done while visiting at Carleton University, also supported by NSERC Canada grants of M. Csörgő, D. A. Dawson and J. N. K. Rao.

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