Theory of Probability and Mathematical Statistics

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

Author(s): Frank Recker
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 76 (2007).
Journal: Theor. Probability and Math. Statist. No. 76 (2008), 159-167.
MSC (2000): Primary 60G40, 90B20
Posted: July 17, 2008
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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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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G40, 90B20

Frank Recker
Affiliation: Department of Mathematics, University of Hagen, D-58084 Hagen, Germany
Email: frank.recker@fernuni-hagen.de

DOI: 10.1090/S0094-9000-08-00740-0
PII: S 0094-9000(08)00740-0
Keywords: Poisson process, stopping time, queuing theory, traffic problems
Received by editor(s): 3/OCT/2005
Posted: July 17, 2008
Copyright of article: Copyright 2008, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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