Analytical And Simulation Study On The Cellular Automation Models For Traffic Flow

With the rapid development of society economy,traffic demand continuously increases.Therefore,transportation problem gradually becomes an emergent world issue,which limits economy development and influences human life greatly.In order to guide the traffic planning,designing,controlling effectively and alleviate the unbalanced supply and demand,the modern traffic flow theory emerged in the 1930s as the times require.Since the birth of the modern traffic flow,more than 100 theoretical models have been proposed by traffic scientists and physicists,from probabilistic theory models in the 1930s-1940s,to kinematic models and car-following models in the 1950s-1960s,and then to fluid-dynamical models in the 1970s-1980s,all of which play a vital role in describing the complex phenomena in traffic.Since the 1990s, cellular automaton(CA) models,with simple rules,clear definition,good expansibility and high computational efficiency,have risen in traffic flow theory as a new force and gradually win the good graces of the traffic scholars and engineers.This paper studies the traffic CA models through both analytics and simulation.On one hand, Totally Asymmetric Simple Exclusion Process(TASEP),the simplest CA model in traffic,is extended to simple road sets.The mean-field analysis and domain-wall theory have been applied to obtain analytic model solutions in order to disclose rich interesting non-equilibrium phenomena analytically and bridge traffic science and non-equilibrium statistics,and thus promote the development of relative disciplines. On the other hand,we select MCD(or FMCD) model that can describe the microscopic structure of the synchronized flow better after comparing the simulation results of three CA models that can reproduce the synchronized flow.Then,MCD model is applied to simulate complex two-lane traffic systems in order to reproduce their real spatio-temporal characteristics,which provides theoretical references for traffic engineering.The contents of the paper are as follows.1.TASEP is applied in two basic road sets:the road with a shortcut and a two-lane intersected road system.The non-equilibrium phenomena in traffic systems are studied with a new in-depth analytic perspective.●Based on the exact solution of the origin single-lane TASEP,the analytic solution of TASEP in the road with a shortcut is obtained with mean-field analysis and domain wall theory.The simulation shows that the phase diagram can be classified into three stationary phases.Because the correlation between the neighboring sites can be neglected,the density profiles corresponding to the three phases are obtained by mean-field analysis,which are in good agreement with the simulation results.For phase boundaries,the mean-field analysis cannot be adopted due to strong correlation.The quantitative domain wall theory is adopted instead to calculate the density profiles on the phase boundaries.The obtained analytic results are in good agreement with the simulation results except slight deviation in the middle main road segment divided by the shortcut.●In the two-lane intersected system,the spontaneous symmetry breaking phenomena occurs surprisingly.The qualitative domain-wall theory is adopted to explain the reason why it occurs.Furthermore,the value of the phase boundary is obtained by mean-field analysis,which is in good agreement with the simulation results.Finally,we investigate the lane-changing effect at the intersection on spontaneous symmetry breaking.It is found that the spontaneous symmetry breaking phenomena disappears if the lane-changing probability exceeds a critical value.2.The synchronized flow is investigated in detail through simulation.Firstly, through comparing and analyzing the simulation results of three CA models that can reproduce the synchronized flow,we conclude that the steady model solutions occupy a two-dimension region in the flow-density plane is a necessary condition for a CA model to reproduce the synchronized flow well.The different mechanism of different models to satisfy the condition has great impact on the microscopic structure of the traffic states.For example,the explicit and implicit mechanism of the KKW model and Lee model to homogenize the traffic flow makes the obtained synchronized flow so homogenous that its microscopic structure deviates from the empirical results.However,the mechanism of MCD (or FMCD) model is that a vehicle can keep its velocity unchanged in certain distance determined by its brake light.Therefore,the microscopic structure of the synchronized flow in MCD model is relatively in better agreement with the empirical results.Then,MCD model is applied to describe two-lane complex traffic system,which can solve the problem that most previous two-lane CA models,in the frame-work of the fundamental diagram approach,cannot reproduce the real spatio-temporal features.●For two-lane homogeneous system,due to the lane-changing effect,the incompact wide moving jams,whose outflow can be either free flow or the synchronized flow,are obtained.It agrees with the empirical results but cannot be obtained in single-lane MCD model.Moreover,the lane-changing frequency against density in previous work deviates from the empirical results,however,in two-lane MCD model,the obtained lane-changing frequency agrees well with the empirical results.Finally,we improve the symmetric lane-changing rules by restricting the lane change of the stopped vehicles,which results in higher road capacity.It is the first time that asymmetric traffic behavior can be maintained under symmetric lane changing rules.●Considering the great impact of the bus system on the spatio-temporal characteristics of the whole traffic system,we investigate a heterogeneous two-lane traffic system consisting of the mixture of buses and cars.Due to the influence of the buses,the whole density range can be classified into four regions,i.e.,the system can be in four states.It is also found that due to the interaction of the cars,the bus clusters gradually disappear with the increase of the car density.Moreover,we study the road capacity under different sets of the number of bus stops with fixed number of buses and an optimal number is suggested.3.A preliminary study on the intelligent transportation systems has been conducted. It is the first time that a hybrid model of the CA model and car-following model is proposed to study the characteristics of the mixed traffic of the adaptive cruise control vehicles and the manual vehicles,which not only removes the artificial velocity fluctuation in the CA model for ACC vehicles, but also maintains the ability to simulate the probabilistic characteristics of the phase transitions among the three traffic states.Moreover,We propose a new range policy for ACC vehicles,which not only maintains the advantages of the constant time headway policy and the nonlinear range policy,but also overcomes their shortcomings,for better design in ACC vehicles.