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The untraceable events method for absorbing processes

Part of: Special processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

Toshinao Nakatsuka
Toshinao Nakatsuka*
Affiliation:
Tokyo Metropolitan University
*
∗Postal address: Faculty of Urban Liberal Arts, Tokyo Metropolitan University, 192-0397 Tokyo, Japan. Email address: tnaka@comp.metro-u.ac.jp
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Abstract

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In this paper we propose a new method of determining the stability of queueing systems. We attain it using the absorbing process and introduce the untraceable events method to show the existence of the absorbing process. The advantage of our method is that we are able to discuss the stability of various variables for both discrete and continuous parameters in a general framework with nonstationary input. An untraceable event has the property that the state loses the memory of its origin. In a concrete model, we use the boundedness of the state at an epoch in time with respect to the initial condition and choose the form of the untraceable event corresponding to the input distribution.

Keywords

Absorbing processuntraceable eventBorovkov eventcontinuous-time parameterasymptotic mean stationarityqueueing system

MSC classification

Primary: 60B10: Convergence of probability measures
Secondary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 652 - 664
Copyright
© Applied Probability Trust 2006 

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