Cellular automata models for synchronized traffic flow

Bifurcation analysis and control of improved traffic flow model considering the effect of strong winds

In recent years, the problem of traffic congestion has become increasingly serious, and research on traffic system control has become a new hotspot. Studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable support points can alleviate traffic congestion from a new perspective. This article improves the full speed differential model considering strong wind models from the perspective of bifurcation control to adjust traffic flow. This article theoretically proves the existence conditions of Hopf bifurcation and saddle node bifurcation in the model and finds the stability mutation point of the transportation system stability. A nonlinear system feedback controller was designed for unstable bifurcation points using Chebyshev polynomial approximation and random feedback control methods. Without changing the system equilibrium point, the advance, delay, and elimination of Hopf bifurcation were achieved, and the abrupt behavior of the transportation system was controlled, thereby alleviating traffic congestion. This article explains the changes in the stability of complex transportation systems from the perspective of bifurcation analysis, which can better capture the characteristics of traffic flow. By adjusting the control parameters in the feedback controller, the influence of boundary conditions on the stability of the transportation system is fully described, and the influence of unstable focal points and saddle points on the system is suppressed, thereby slowing down the traffic flow. In addition, unstable bifurcation points can be eliminated, and the Hopf bifurcation can be controlled to advance, delay, and disappear, thereby achieving control over the stable behavior of the transportation system. This helps alleviate traffic congestion and also helps describe actual traffic phenomena.

Cellular automata can classify data by inducing trajectory phase coexistence

We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the number of state changes that occur in a trajectory initiated from the image. When the number of time steps of the automaton is a trainable parameter, the search scheme identifies automata that generate a population of dynamical trajectories displaying high or low activity, depending on initial conditions. Automata of this nature behave as nonlinear activation functions with an output that is effectively binary, resembling an emergent version of a spiking neuron.

Physics of microscopic vehicular traffic prediction for automated driving

With the use of microscopic traffic simulations, physical features of microscopic traffic prediction for automated driving that should improve traffic harmonization and safety have been found: During a short-time prediction horizon (about 10 s), online prediction of the locations and speeds of all vehicles in some limited area around the automated-driving vehicle is possible; this enables the automated vehicle control in complex traffic situations in which the automated-driving vehicle is not able to make a decision based on current traffic information without the use of the microscopic traffic prediction. Through a more detailed analysis of an unsignalized city intersection, when the automated vehicle wants to turn right from a secondary road onto the priority road, the statistical physics of the effect of a data uncertainty caused by errors in data measurements on the prediction reliability has been studied: (i) probability of the prediction reliability has been found; (ii) there is a critical uncertainty, i.e., a maximum amplitude of errors in data measurements: when the uncertainty does not exceed the critical uncertainty, the prediction reliability probability is equal to 1, otherwise, the prediction is not applicable for a reliable automated vehicle control; (iii) physical characteristics of the microscopic traffic prediction, at which the critical uncertainty can be increased considerably, have been found; and (iv) there is an optimal automated vehicle control at which the critical uncertainty reaches a maximum value.

Traffic flow simulation of modified cellular automata model based on producer-consumer algorithm

With the rise of new technologies such as the Internet of Vehicles and the Internet of Things, research on the intelligent connected vehicle has become a hot topic in contemporary times. The modeling and simulation of traffic flow are mainly used to analyze the characteristics of traffic flow and study the formation and dissipation mechanism of traffic congestion to better guide the real traffic. Cellular automata are suitable for the simulation of complex giant systems. Because of the randomness and discreteness of vehicle driving, cellular automata are often used to model and analyze traffic flow. This article mainly studies the traffic flow formed by intelligent connected vehicles. Based on the traditional NaSch model, the producer-consumer algorithm is introduced to form a multi-buffer vehicle information access mode, and an improved cellular automata model with random updates is constructed. The simulation results show that the improved cellular automata model improves the traffic congestion significantly compared with the original NaSch model in the intelligent network environment, which is consistent with the actual traffic situation. Therefore, the algorithm proposed in this article can effectively simulate the traffic flow characteristics of intelligent connected vehicles, and provide a theoretical basis for solving traffic problems.

Long-range correlations of density fluctuations in the Kerner-Klenov-Wolf cellular automata three-phase traffic flow model

Detrended fluctuation analysis (DFA) is a useful tool to measure the long-range power-law correlations in 1f noise. In this paper, we investigate the power-law dynamics behavior of the density fluctuation time series generated by the famous Kerner-Klenov-Wolf cellular automata model in road traffic. Then the complexities of spatiotemporal, average speed, and the average density have been analyzed in detail. By introducing the DFA method, our main observation is that the free flow and wide moving jam phases correspond to the long-range anticorrelations. On the contrary, at the synchronized flow phase, the long-range correlated property is observed.

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

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.

Relationship between microscopic dynamics in traffic flow and complexity in networks

Complex networks are constructed in the evolution process of traffic flow, and the states of traffic flow are represented by nodes in the network. The traffic dynamics can then be studied by investigating the statistical properties of those networks. According to Kerner's three-phase theory, there are two different phases in congested traffic, synchronized flow and wide moving jam. In the framework of this theory, we study different properties of synchronized flow and moving jam in relation to complex network. Scale-free network is constructed in stop-and-go traffic, i.e., a sequence of moving jams [Chin. Phys. Lett. 10, 2711 (2005)]. In this work, the networks generated in synchronized flow are investigated in detail. Simulation results show that the degree distribution of the networks constructed in synchronized flow has two power law regions, so the distinction in topological structure can really reflect the different dynamics in traffic flow. Furthermore, the real traffic data are investigated by this method, and the results are consistent with the simulations.

Toward an improvement over Kerner-Klenov-Wolf three-phase cellular automaton model

The Kerner-Klenov-Wolf (KKW) three-phase cellular automaton model has a nonrealistic velocity of the upstream front in widening synchronized flow pattern which separates synchronized flow downstream and free flow upstream. This paper presents an improved model, which is a combination of the initial KKW model and a modified Nagel-Schreckenberg (MNS) model. In the improved KKW model, a parameter is introduced to determine the vehicle moves according to the MNS model or the initial KKW model. The improved KKW model can not only simulate the empirical observations as the initial KKW model, but also overcome the nonrealistic velocity problem. The mechanism of the improvement is discussed.

Empirical test for cellular automaton models of traffic flow

Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: (1) models that do not reproduce even qualitatively the most important empirical observations, (2) models that are on a macroscopic level in reasonable agreement with the empirics, and (3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed light on the relevant interactions in traffic flow.

Open boundaries in a cellular automata model for synchronized flow: effects of nonmonotonicity

In this paper, we have discussed the traffic situations arising from the open boundary conditions (OBC) of a cellular automata model that can reproduce the synchronized flow. The model is different from the slow-to-start (STS) model in that the upper branch of the fundamental diagram in the periodic boundary conditions (PBC) is not monotonous but has an extremum. The phase diagram and the fundamental diagram of the model in the OBC are investigated. The results are compared with those of the STS model and those in the PBC. The current in the OBC as well as the density profiles in the different phases is also investigated.