From The Basic Diagram To A Three-phase Traffic Flow Theory

In this dissertation,we investigate the Cellular Automaton(CA)models for traffic flow in the theoretical frameworks of both the traditional Fundamental Diagram Approach and the newly-developed Three-phase Traffic Theory.Traffic and transportation systems,whose level of advancement has become one of the most important criterions in evaluating the modernization of a country,are playing important roles in social economy. However,the relatively weaker traffic system constructions versus the high-speed development of social economy,has become a prominent contradictions throughout the whole world.Traffic congestions have caused serious pollution and huge economic ex penses,which with time are even becoming more and more serious.On the other hand, transportation constructions which lack of scientific directions,are not only extremely expensive but also ineffective at all.Therefore,one after another,the developed countries in the world are all devoted into the research programs of traffic engineering and traffic flow theory,in order to discover the basic rules of traffic flow,take hold of proper strategies in traffic managements,and furthermore,to have their transportation systems managed and optimized scientifically.On the other hand,in the viewpoint of academic research,as a classical type of selfdriven systems which are far from equilibrium,traffic flow systems exhibit typical laws of non-equilibrium many body systems evolution with complex interactions,which are ubiquitous in human society.Traffic flow research may help promoting the interdisciplinary developments among statistical physics,fluid mechanics,nonlinear dynamics,application mathematics,traffic engineering,and so on.Therefore,the theoretical research on traffic flow is significant not only in engineering applications,but also in scientific discoveries. And traffic flow modeling,as a important part of theoretical research,provides us available approaches to have the traffic phenomena reproduced and interpreted.Among the modeling approaches,cellular automaton models(CA)is especially popular because of its simple structure and discrete spatial and temporal variables,which makes it easy to simulate the dynamical processes of a huge number of interacting vehicles.Currently,there are two different theoretical frameworks of traffic flow which dominate this area,i.e.,the fundamental diagram approach and the three-phase traffic theory. In both frameworks,researchers have established realistic and logical traffic flow models, and reproduced many traffic phenomena consistent with empirical findings.As the current frontier of theoretical research of traffic flow,three-phase traffic theory distinguished all the traffic states into three traffic phases,i.e.,the free flow phase,the synchronized flow phase and the wide moving jams phase.Three-phase traffic approach can reproduce more realistic results comparing to the fundamental diagram approach when dealing with the bottleneck-induced congestion patterns.As a results,it is gradually recognized by researchers all over the world.In this dissertation,on top of a brief introduction to the research background of traffic flow theory,including the outlines of both the fundamental diagram approach and the three-phase traffic theory,we introduce our own research accomplishments,summarized as following:(1)With cellular automaton modeling approach,we made realizations of the traffic mechanism proposed by Kaupu(z)s et.al.,in which the slow-to-start(s2s)action of each vehicle depends on the length of the cluster which contains the corresponding vehicle.As a result,we established an improved s2s traffic model,which as well as the previous s2s models,can reproduce the hysteresis effect,the metastable states, and the phase-separated phenomenon of traffic.On the other hand,the improved model has the following improved characteristics.First,the improved s2s rules produce self-adaptation effect,which makes the dissolving process of initial jams more rapid and fluent comparing to the same process in previous s2s models.Furthermore, the improved model effectively reduces the systematic perturbations in which little jams continuously form,dissolve and then reform.As a result,it promoted the traffic efficiency remarkably.Second,the improved model characteristically exhibits three distinguishable periods during the dissolving process of initial jams,i.e.,the linearly declining head part,the exponentially declining middle part, and the approximately power-law declining tail,which dynamically reflects the microscopic statistical characters in great details.Third,the improved model exhibits the cluster-size distributions having a single peak at low densities,or double peaks at high densities,which discovers the different origins of the phase-separations corresponding to the two different peaks.Furthermore,the diffusion of data points in the distribution is much less than in previous models,which reflects more explicit characters of phase-separation.This work has been published on Chinese Physics Vol.16,No.11,2007。(2)Combining the NS CA model with the classical car-following model,we got an improved CA model which considers the velocity-difference effect between successive vehicles.This model shows some particular characteristics in numerical simulations.First,it simulates an abnormal hysteresis effect in which the flux relations between homogeneous and inhomogeneous traffic are reversed.Second,the fundamental diagram of this model has two maximums in flux,showing as a doublepeak structure.Through investigations on the spatial-temporal evolutions and the correlation functions,we find both the two points listed above are related to the emergence of one kind of "homogeneous congested traffic",which is quite similar to the synchronized flow in both macroscopic characters and microscopic characters. This model discovers that in some particular cases,inhomogeneous traffic flow may take better utilizations of the traffic capacity of the system comparing to homogeneous flow.On the other hand,although it is essentially a model in the framework of fundamental diagram approach,however,it could also be understood as an intermediate model between the fundamental diagram approach and the three-phase traffic theory,which has shed some light on the research and comparison between the two theoretical frameworks of traffic.This work has been published on Physica A 386(2007):397-406.(3)On top of the previous work mentioned above,we have the model further developed. We introduced the slow-to-start effect into the model,in order to induce the spontaneously phase transition from synchronized flow to wide moving jams.On the other hand,we directly dispersed the equation of the classical car-following model,and incorporates the velocity-difference effect into our model.As a result, we have established a traffic flow model in the framework of three-phase traffic theory. This model can simulate the three traffic phases and the spontaneous first-order phase transition from synchronized flow to wide moving jams rightly.On an open road with isolated on-ramp bottleneck,this model simulates five traffic congested patterns,including General Pattern(GP),Widening Synchronized Pattern(WSP), Dissolving General Pattern(DGP),Localized Synchronized Flow Pattern(LSP)and Synchronized Pattern Alternation of Free and Synchronized Flow(ASP).All these congested patterns are consistent with empirical findings and theoretical deductions of the three-phase traffic theory.This work has accomplished the most important step from the fundamental diagram approach to the three-phase traffic theory.It has been published on Phys.Rev.E 76,026105(2007)。(4)Based on the previous two works,in which we have established a three-phase traffic model,we further studied some unresolved problems previously.In order to reproduce the spontaneous first-order phase transition from free flow to synchronized flow,and the related "moving synchronized pattern"(MSP),which are absent in the previous model,we proposed a limitation of the interaction range between successive vehicles.In the improved model,only vehicles being close enough to each other can have interactions.As a result,the improved model successfully reproduced the expected items mentioned above.The fundamental diagram of the improved model exhibits typical double-Z characteristics of three-phase traffic models, which is well consistent with Kerner's theory.Furthermore,we studied the correlation functions for free flow and synchronized flow respectively.The analysis results are not only well consistent with empirical findings,but also good illustrations to the nontrivial characteristics of free flow especially.Besides,we also studied the time headway distributions and the optimal velocity(OV)functions of the model.Comparing to previous models in the framework of three-phase traffic theory, this model simulates similar time-headway distributions,which are only partly consistent with empirical results.But the simulation results of the OV functions are greatly improved in this model.The simulations results are in great accordance with empirical findings.Therefore,we have accomplished a successful modeling work in the framework of three-phase traffic theory,in which we have established a CA model whose simulation results are not only consistent with empirical resuits in macroscopic features,but also a great improvement in microscopic features comparing to previous models.This work is currently under the review of Physical Review E.