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Theory of Probability and Mathematical Statistics

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The distribution of a random sum of exponentials with an application to a traffic problem

Author: Frank Recker
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 76 (2007).
Journal: Theor. Probability and Math. Statist. 76 (2008), 159-167
MSC (2000): Primary 60G40, 90B20
Published electronically: July 17, 2008
MathSciNet review: 2368748
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Abstract: We study a random sum of exponentially distributed random variables. The stopping time is defined to be the first realization that is greater than or equal to a given constant. We will derive an expression for the distribution function of this sum. This has applications in determining the waiting time for a large gap in a Poisson process. As an example, we will give a traffic problem, where such a waiting time occurs.

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Additional Information

Frank Recker
Affiliation: Department of Mathematics, University of Hagen, D-58084 Hagen, Germany

Keywords: Poisson process, stopping time, queuing theory, traffic problems
Received by editor(s): October 3, 2005
Published electronically: July 17, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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