Cellular-automaton model with velocity adaptation in the framework of Kerner’s three-phase traffic theory

Abstract

In this paper, we propose a cellular automata (CA) model for traffic flow in the framework of Kerner's three-phase traffic theory. We mainly consider the velocity-difference effect on the randomization of vehicles. The presented model is equivalent to a combination of two CA models, i.e., the Kerner-Klenov-Wolf (KKW) CA model and the Nagel-Schreckenberg (NS) CA model with slow-to-start effect. With a given probability, vehicle dynamical rules are changed over time randomly between the rules of the NS model and the rules of the KKW model. Due to the rules of the KKW model, the speed adaptation effect of three-phase traffic theory is automatically taken into account and our model can show synchronized flow. Due to the rules of the NS model, our model can show wide moving jams. The effect of "switching" from the rules of the KKW model to the rules of the NS model provides equivalent effects to the "acceleration noise" in the KKW model. Numerical simulations are performed for both periodic and open boundaries conditions. The results are consistent with the well-known results of the three-phase traffic theory published before.

Discontinuous transition from free flow to synchronized flow induced by short-range interaction between vehicles in a three-phase traffic flow model

“…[59] that Eq. (4) can be seen as another mathematical formulation of the speed-adaptation effect firstly proposed by Kerner in Refs.…”

“…These models were designed by considering different aspects of possible vehicular traffic dynamics, and most of them were represented by cellular automaton (CA) modeling approach. In 2007, Gao, Jiang and Hu et al proposed other possible driving mechanics in their CA traffic flow models [58,59]. These models focus on the influence of the velocitydifference between two successive vehicles on the randomization process of the following one (so that we call them ''Velocity-difference effect (VDE)'' series models in this paper).…”

“…As well as the previous VDE-II model in Ref. [59], the VDE-III model is also equivalent to a combination of the KKW CA model [41] and the Nagel-Schreckenberg (NS) model with the slow-to-start effect [30,60] (see Eqs. (5) and (6) in Ref.…”

“…[59]. In the VDE-II model, we execute the velocity-difference effect by changing the deceleration extent instead of the randomization probability in the randomization process.…”

“…Let t st,n denote the stop time of vehicle n (t st,n = m means vehicle n has been stopping for m time steps currently) and t c denote the time threshold of slow-to-start effect [56,57,59,60], the randomization probability p n (t + 1) and the deceleration extent v are determined by the following formulations:…”