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On road traffic with free overtaking

Published online by Cambridge University Press:  14 July 2016

Torbjörn Thedéen
Torbjörn Thedéen*
Affiliation:
Royal Institute of Technology, Stockholm
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Abstract

The cars are considered as points on an infinite road with no intersections. They can overtake each other without any delay and they travel at constant speeds. These are independent identically distributed random variables also independent of the initial positions of the cars. The main purpose of the paper is the study of the asymptotic distribution for the number of overtakings (and/or meetings) in increasing rectangles in the time-road plane. Under the assumption of (weighted) Poisson distributed cars along the time-axis we deduce the asymptotic distribution of the standardized number of overtakings (and/or meetings) for large rectangles in the time-road plane. Lastly we shall indicate an application of the results.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 524 - 549
Copyright
Copyright © Applied Probability Trust 

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