Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G40, 90B20

Retrieve articles in all journals with MSC (2000): 60G40, 90B20


Additional Information

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

DOI: http://dx.doi.org/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): October 3, 2005
Published electronically: July 17, 2008
Article copyright: © Copyright 2008 American Mathematical Society