On road traffic with free overtaking
- 1 December 1969
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 6 (3) , 524-549
- https://doi.org/10.2307/3212100
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.Keywords
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