Cellular Automaton Model with Dynamical 2D Speed-Gap Relation

This paper proposes an improved cellular automaton traffic flow model based on the brake light model, taking into account that the desired time gap of vehicles is larger than one second. Although the hypothetical steady state of vehicles in the deterministic limit corresponds to a unique relationship between speeds and gaps in the proposed model, the traffic states of vehicles dynamically span a two-dimensional region in the plane of speed versus gap, due to the various randomizations. We show that our model reproduces (i) the free flow, synchronized flow, wide moving jams, as well as transitions among the three phases; (ii) the evolution features of disturbances and the spatiotemporal patterns in a car-following platoon; (iii) the empirical time series of traffic speed obtained from Next Generation Simulation data. Furthermore, the basic feature of time headway distribution is also qualitatively reproduced. Therefore, we argue that a model has the potential to reproduce the empirical and experimental features of traffic flow, provided that the traffic states can dynamically span a 2D speed-gap region.