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The uncontrolled traffic merge

Published online by Cambridge University Press:  14 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
CSIRO Division of Mathematics and Statistics, Sydney
*
∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, N.S.W. 2070, Australia.
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Abstract

The merging of n independent traffic streams is studied. The arrival processes comprise random sized bunches of cars, the bunches being separated in time by random sized gaps. Within each bunch, cars are spaced at one time unit apart. Under a distributional assumption on the inter-bunch gaps exact formulae are found for (a) the mean delay to cars, (b) the first two moments of the post-merge bunch size, and (c) the distribution of the inter-bunch gaps in the post-merge process. It is shown that the distributional assumption is realistic and moreover that the distribution of (c) is of the same form. The arrival bunches have general size distribution with finite mean and variance.

Keywords

TRAFFIC MERGECONGESTIONQUEUEINGPOINT PROCESSESM/D/1 QUEUEPOLLACZEK-HINČIN FORMULA
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 384 - 392
Copyright
Copyright © Applied Probability Trust 1979 

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References

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