The uncontrolled traffic merge

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.