Properties of Cowan’s M3 Headway Distribution

Abstract

Cowan’s M3 distribution has been used in several studies on unsignalized intersections, especially roundabouts. It allows separate analysis of follower and nonfollower headways, and it is simple enough for models of considerable complexity. Although M3 gives a simplistic model for short headways, it has many desirable properties as a headway distribution. It is possible to estimate its parameters with simple methods and with reasonable accuracy, and the estimated models give good results in the capacity analysis of unsignalized intersections. Described in this paper are the basic statistical properties of M3, and the accuracy of the method of moments and least-squares parameter estimators is evaluated. The validity of M3 in unsignalized intersection capacity analysis is evaluated by a Monte Carlo simulation with samples from M3 and semi-Poisson distributions.