Modeling Spacing Distribution of Queuing Vehicles in Front of a Signalized Junction Using Random-Matrix Theory

Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to explain the spacing distribution of queuing vehicles in front of a signalized junction based on random-matrix theory. We show that the recently measured spacing distribution data well fit the spacing distribution of a Gaussian symplectic ensemble (GSE). These results are also compared with the spacing distribution observed for car parking problem. Why vehicle-stationary-queuing and vehicle-parking have different spacing distributions (GSE vs GUE) seems to lie in the difference of driving patterns

A Markov Process Inspired Cellular Automata Model of Road Traffic

To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed distribution of practical gaps. The multiformity of this Markov process provides the model enough flexibility to describe various driving behaviors. Two examples are given to show how to specialize it for different scenarios: usually mentioned flows on freeways and start-up flows at signalized intersections. The agreement between the empirical observations and the simulation results suggests the soundness of this new approach.Comment: revised according to the helpful comments from the anonymous reviewer