The Oversaturated Signalized Intersection—Some Probabilistic Aspects

In two papers by C. J. Ancker, Jr., A. F. Gafarian, and R. K. Gray, the structure of the headways at the passage of an oversaturated signalized intersection were studied. The statistical analysis performed by these authors seems to confirm the hypothesis that these headways are independent random variables. In this paper we consider the following simple model. Let the spacings and reaction times of the vehicles stopped at the intersection all be independent and let the trajectory relative to the start position and start time be the same for all stopped vehicles. It is shown that the headways at the intersection are independent if and only if this trajectory is linear in a certain region specified in the paper.