A stochastic model of congestion caused by speed differences

We study interaction between the trips of two types of drivers on a two-lane road who differ by their desired speeds. The difference in desired speeds causes congestion, because slow drivers force fast drivers to reduce their speed. An interesting aspect of this type of congestion is that results with respect to tolling are very different from those of the classical Pigou-Knight model where the marginal external costs are an increasing function of the number of road users. In our model we find the opposite result: the marginal external costs of slow drivers are a decreasing function of the number of slow drivers. This leads to rather different policy recommendations. In many situations either laissez faire (no tolling or traffic restrictions) or prohibition of slow drivers to enter the road is in practice (i.e. taking into account costs associated with tolling) the optimal policy. This conclusion hardly changes if the possibility of overtaking is introduced into the model.