Phase Transition Phenomenon In Traffic Flow Cellular Automata Model

Traffic transport capacity is a key factor restricting the speed of a country's urbanization and modernization, and has played an important role in supporting the development of the national economy. The high transport ability can reduce people's travel time, improve work efficiency, and promote convenient circulation of the materials and human resources. In the modern society, the transportation situation of a country or city has already been an important index to measure the region's growth potential. Although the global governments have paid much attention to the transportation improvement and spent enormous amounts on it, the traffic jams phenomena still appear quite often and become one of the major problems troubling governments. Around the world, the frequent traffic congestion, traffic accidents and problem of exhaust gas emission polluting environment have directly or indirectly caused a huge economic loss. For example in the "11th five-year plan" period of China, the transportation development has gotten the outstanding achievement and been the fastest among past periods, regardless of traffic facilities amount, scale, or transportation capacity supply etc. But due to the amounts of private cars maintaining the even more tremendous growth speed, the roads supply is still not enough comparing to the vehicles demand. Hence in big cities during the rush time, it is common to see hours of traffic jams. Every year the economic losses caused by traffic congestions can reach to hundreds of billions Yuan.In order to solve the urban traffic problems and improve the performance of the transportation system in our country, on the one hand, it needs to transform road network system, widen the roads and traffic facilities, and add the constructions such as hardware. On the other hand, it also needs to adopt scientific traffic management and the modern high technology for improving the existing road traffic performance, the whole road management efficiency, and realizing the rationality and validity of urban traffic management. Above two respects are complementing each other and can be both equal important. The traffic flow as an advanced scientific theory is just to investigate various complex phenomena and their causes in urban or highway transportation, understand the nature of traffic problems and solve them optimistically. In one words, sufficiently utilizing the existing traffic facilities, rationally using the limited traffic resources, and scientifically managing and controlling traffic is the only way to relieve the pressure of rapidly increasing traffic demand, and eventually solve the traffic problems during the country development. For this reason, the traffic flow theory is emerging at the end of last twentieth century, and especially in recent years has attracted many researchers'attention of various disciplines, covering the fluid mechanics, system science, nonlinear science, theoretical physics, applied mathematics, traffic engineering, computer information science, statistics, and so on.The objective of traffic flow theory research is using modern scientific knowledge with measured data, accurately describing the traffic characteristics, establishing and proposing proper mathematical model and theoretical analysis, revealing the essence of traffic flow phenomena through numerical simulation and parameter identification, providing reliable transportation management strategy, developing the applicable procedures and computer packages, and eventually achieving real-time monitoring and optimization of the transport system. And besides above important practical value, traffic flow theory study also has profound scientific significance. The transportation system is composed of a number of discrete vehicles moving in complex road network. The relations of vehicles and roads can be regard as a kind of complicated nonlinear evolution in unbalanced self-driven system. Until now there has not been a strict and mature fundamental theory to describe such complex system. Therefore, the research of traffic flow theory can provide an angle to deepen the understanding of complex science and promote the multidisciplinary development.After studying the extensive literature about traffic flow theory and based on previous researchers'work, the authors of this paper propose some more realistic two-dimensional and one-dimensional traffic flow cellular automata model, and then give detailed computer simulations and theoretical analyses. These modified models have shown some new results, such as new stable equilibrium and phase transition phenomenon etc. This series work is expected to establish the theory to understand the essence rule behind the traffic surface phenomenon, and then in turn guide the practice of urban or highway traffic management, planning and design process. The main content of this paper includes three aspects of research work as follows.(1) We introduce the urban traffic flow model considering the impact of traffic lights period, which is on the basis of the classical two-dimensional traffic flow cellular automata model. The simulation results of the new model show that besides the equilibrium phases which have been found in previous literature, there is another stable equilibrium state which has not been reported. This new phase consists of the free flow pattern and congestion area, and appears near the density region corresponding to the critical phase transition from high speed to low speed phase. And further we find that the system critical densities have non-monotonous relation with the traffic light periods, indicating there is an optimal traffic light period maximizing the traffic capacity for certain system. Finally, we qualitatively explain the formation and dynamic stability of the free flow and jam separation phase, and give the theoretical relations of the system average velocity to vehicle density and the critical density to traffic light period using the mean-field approximation method. The analytical solutions accord with the computer simulation results very well, except in the short traffic light period condition. Then we have discussed the reason of relative errors. The significance of this work is for designing the optimal traffic light period strategy through revealing the impact of period change, and making the system to contain the maximum number of vehicles without changing the urban road network structure.(2) We introduced the two-dimensional traffic flow model taking into account the drivers'game behaviors. This model is also on the basis of the classical model, and then considers the actual drivers'micro psychology. Supposing two cross directional driving cars encounter in the crossroad without installing traffic lights, finally there must be at least one car stopping in order to avoid crash. This situation can be simulated through the drivers'game behaviors, which can be called cooperator and defector in term of game theory. The cooperator means the driver whom will decelerate and consult when meeting another direction car. And the defector means the driver whom will accelerate and try to pass through when encountering another car. The simulation of this traffic flow model finds a near free flow random phase locating between free flow and jammed phases. It is a new equilibrium state with high average vehicles velocity just below one. And further, it is found that adding some defector drivers and increasing transform probability of defector to cooperator could increase the system critical vehicle density and make the transportation more efficiency. The significance of this work is for introducing the game behaviors to the traffic flow model and finding that the more cooperator drivers the smoother of transportation, which provides the scientific support of encouraging the drivers to be mutual amicable.(3) We introduce the hybrid intelligent traffic flow model with vehicle speed optimization based on leading vehicles'information. This model is proposed for the practical need of the modern intelligent transportation system with the development of high communication technology. Recently there have been cars equipping adaptive cruise control system, which can collect the information of the positions and velocities of vehicles in the road. Thus it is possible to calculate the optimal velocity for each car based on vehicles'information. From this idea, we design the model to analyze the permitted instant maximum speed of the traffic system according to the leading cars'information as input parameters. Through numerical simulation, this model also finds the phase transition phenomenon, of which the traffic flux first increases linearly with the increasing vehicle density and then decreases until to zero after critical density. And then it is found that there is an optimal intelligent cars ratio just according to the maximum traffic flux in the condition that the vehicle density is below the certain threshold of the hybrid system. Finally, we give the accurate theoretical analysis of the relationship of critical density to the sight and ratio of the intelligent vehicles. The significance of this work is for proposing a hybrid intelligent traffic flow model with vehicle speed optimization and certifying the feasibility of adding the intelligent cars for improving the transportation ability. And in addition, it properly instructs us to design the right most effective traffic strategy according to the present actual road situation.