Simple probabilistic model for state transition analysis of a roundabout

抄録

A probabilistic model is proposed to investigate the time-evolution of traffic flow on the circular lane of a roundabout, which is located at the intersection of three approach roads. The circular lane is divided into six cells, and the probability that each cell is occupied by a vehicle is discussed. A six-dimensional vector is introduced to indicate the probability of occupancy of each cell at any particular instant. A set of simple assumptions related to traffic rules are used to derive a linear difference equation that governs the sequential motion of the probability vector. The difference equation is shown to have a uniform equilibrium that is unique and stable. In the case where the equilibrium is replaced by another due to parameter change in relation to environmental fluctuation, several different modes are found in the process of transition to the new steady state.