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A note on level-crossing analysis for the excess, age, and spread distributions

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Tsuyoshi Katayama
Tsuyoshi Katayama*
Affiliation:
Toyama Prefectural University
*
∗ Postal address: Department of Electronics and Informatics, Faculty of Engineering, Toyama Prefectural University, Kosugi-Machi, Toyama 939-0398, Japan. Email address: katayama@pu-toyama.ac.jp
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Abstract

In this paper, we show that the time-average distributions of excess, age, and spread are given by the solution of first-order differential equations. These differential equations can be directly derived in a simple, unified way using a general level-crossing formula based on the balance of up and down crossings on sample paths, which may be helpful for the intuitive interpretation.

Keywords

Renewal processlevel-crossing methoddifferential equationtime average

MSC classification

Primary: 60G17: Sample path properties 60K05: Renewal theory 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 896 - 900
Copyright
Copyright © Applied Probability Trust 2002 

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