Distribution of Gaps and Blocks in a Traffic Stream

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Abstract
This paper studies some of the theoretical questions of large openings or gaps in a single stream of traffic. A gap in the traffic stream is defined as a headway between vehicles greater than or equal to some minimum size—say x. Several authors have studied the probability distribution of the wait that a randomly located observer must endure before he finds a gap. This paper, while briefly reviewing the solutions of this well-known problem, is primarily concerned with expressions for (i) the distribution of gap sizes, (ii) the distribution of spacings between vehicles and gaps, (iii) the mean and variance of intervehicle and intergap spacings, (iv) the stationary flow rates of gaps, and (v) the distribution of blocked and unblocked periods. It is assumed that the origin of measurements may be located (i) with the passing of a vehicle, (ii) at the beginning of a gap, or (iii) at random. It is also assumed that the distribution of intervehicle spacings are independently, but identically, distributed random variables.

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