The movement of traffic past a point is compared to the output of a queuing system having random input. A generalization of the queue output model leads to a suitable headway model: this model is a mixture of two distributions, representing following and nonfollowing headways, in appropriate proportions. Thin model is compared with several others that have been suggested; when used with a lognormal distribution of following headways, it gives the best overall fit to data from the M4 motorway, England, and two-way roads in Indiana, USA. For each site, the parameters of the following headway distribution can be assumed constant. The mean following headways are 1.3 sec and 1.6 sec for the M4 fast and slow lanes respectively, and 2 sec for the Indiana sites. The standard deviation of logarithms of following headways is 0.4 for both M4 lanes and 0.45 for the Indiana sites. For most samples, the reciprocal of the mean interbunch gap λ can be approximated by λ = λ* − 1/2 λ*3/2, where λ* is the flow rate, and the proportion of the following vehicles ψ can be approximated by ψ = ρ − 1/2(ρ − 1)λ*3/2, where ρ is the traffic intensity.