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From matchbox to bottle: a storage problem

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ludwig Baringhaus  and
Rudolf Grübel
Ludwig Baringhaus*
Affiliation:
Universität Hannover
Rudolf Grübel*
Affiliation:
Universität Hannover
*
∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany.
∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany.
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Abstract

We generalize Banach's matchbox problem: demands of random size are made on one of two containers, both initially with content t, where the container is selected at random in the successive steps. Let Zt be the content of the other container at the moment when the selected container is found to be insufficient. We obtain the asymptotic distribution of Zt as t → ∞ under quite general conditions. The case of exponentially distributed demands is considered in more detail.

Keywords

Asymptotic normalityBessel functionsconvergence in distributionexponential distributionKnuth's old sumrenewal theory

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60F05: Central limit and other weak theorems 60K05: Renewal theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 650 - 656
Copyright
Copyright © Applied Probability Trust 2002 

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