Since the widely used Poisson law describes vehicular distribution quite well for very low traffic flow rates, but deviates significantly from reality when the flow rate rises above a few dozen vehicles per hour per lane, mr. Schuhl develops a description of the vehicular distribution for a traffic stream composed of two distinct Poisson flows through the application of probability theory. The entire traffic stream is considered as having a set of gaps containing two subsets. Each subset has a distinct mean and both obey some Poisson-type law. Assuming that vehicles can be represented by points on a straight line, the probability of a gap greater than some fixed value is developed in general terms and modified to consider a lower bound on the size of the gap. The modified model is fit to two data samples and compared with a Poisson fit in one case. Schuhl's equation provides a much closer fit than does the Poisson law. Further mathematical relations developed are: (1) the probability of a fixed time interval, selected at random, containing no vehicles being bounded on one side by a vehicle, (2) the probability of a fixed time interval, selected at random, containing exactly n vehicles, (3) the probable delay to a vehicle waiting for a greater gap in the opposing lane of traffic, and (4) the probability of finding a platoon of vehicles with a given number of vehicles in it where a platoon is defined by the consecutive vehicles separated by a gap less than some given value.
Abstract