A probabilistic model for the behaviour of traffic at a roundabout

A discrete-time, Markov chain model is proposed to describe the behaviour of traffic travelling on a single-lane roundabout and queueing on approach roads to enter the roundabout. A general origin-destination matrix is allowed for trip ends, there is an arbitrary number of approach roads and there is room for a general number of vehicles on each weaving section. Attention is given to the equilibrium régime at an approach subject to heavy traffic conditions. It is shown that for such an approach the moments of the distribution of the length of the queue of waiting vehicles may be found by a heavy traffic approximation.