Modeling Traffic Flow And Controling Traffic Congestion With Application Of Intelligent Transportation System

Currently, traffic problem has become an important issue, which draws generalconcern of the international community. Over the past decades, a lot of scholars havebeen conducting extensive research on this subject, proposing a variety of traffic flowtheories, and yielding an enormous amount of results. In this dissertation, based on thecar-following model and lattice hydrodynamic model, several improved mathematicalmodels are presented by using the concept of Intelligent Transportation System (ITS)and the feedback control theory, and corresponding theoretical analysis and numericalsimulation are performed so as to explore the intrinsic mechanism of traffic congestionand the measures for reducing traffic jams.The main contents of the dissertation are as follows.1. The traffic congestion control of single-lane traffic is discussed via a modifiedcoupled map car-following model integrated with the ITS and the thoery offeedback control.An improved coupled map car-following model is proposed with the application ofITS to describe the dynamics of single-lane traffic and the control of the trafficcongestion. Based on the theory of feedback control, the stability criteria are givenwhen the leading vehicle's speed is changed. The theoretical results show thatconsidering more information about preceding vehicles could lead to the improvementof the traffic flow stability, i.e., the stability conditions is obviously weakened. Thevalidity and correctness of the theoretical analysis is confirmed by direct numericalsimulations. By comparing the present results with the previous related studies, aconclusion is drawn that the application of ITS could reduce or buffer the trafficcongestion effectively.2. The influence of the following car on the control of traffic congestion and thenumber of effective preceeding vehicles affecting traffic are studied. With the application of ITS information, a modified coupled map car-followingmodel is proposed to describe the dynamical behavior of vehicles moving along asingle-lane road. It is assumed that there exists a vehicle-bound navigation systemproviding each vehicle with the information about its preceding and following vehicles.Based on a principle of feedback control, the stability criteria are provided as the speedof the preceding vehicle changes. Through calculation, we conclude that the informationof three preceding cars is sufficient for suppressing the traffic jam and the influence ofmore preceding vehicles could be neglected. Besides that, the affecting coefficient of thepreceeding vehicles on the present vehicle is given. During numerical simulations, tentypical kinds of vehicles are distributed randomly on the road. The correspondingnumerical simulations confirm the correctness of the theoretical analysis. Compared withprevious researches concerning congestion control, the control strategy of consideringmore information about the preceeding and following vehicles from ITS is moreeffective in avoiding the formation of traffic jam.3. The influence of other factors on traffic jam control is discussed by using acoupled map car-following model.With the consideration of the effect of vehicles (or non-motor vehicles) on otherlanes without isolation belts, three modified coupled map car-following models areconstructed. According to the feedback control theory, the stability conditions of thecurrent vehicle influenced by vehicles on other lanes are gained. The correspondingnumerical simulations confirm the correctness of the theoretical analysis. It can be foundthat on urban roads without isolation belts, the headway between the preceeding andfollowing vehicles on the current lane needs to be considered, and the influence ofvehicles on other lanes (the transverse distance and the longitudinal distance) also needsto be emphasized. It is worthy mentioning that among the three lanes of a road, thestability of cars on the middle lane is weaker than that on the other two lanes. Finally,some suggestions for vehicle travelling are made. 4. A modified car-following model is presented, in which the driver's sensitivity isaffected by the road conditions.Owing to the real traffic that the drivers'sensitivities are different for differentspeeds and road conditions, two car-following models areestablished: one is only relatedto the headway of cars besides the sensitivity, and the other is also considering thevelocity difference including the study mentioned above. In both models, a smallparameter is added to the original sensitivity. Based on the Hurwiz stability theory, theallowable variation ranges of this parameter, especially at different velocities areobtained. Comparing these two models, we can see clearly that the model with thecontrol of velocity difference could increase the stability of traffic flow.5. With ITS and lattice hydrodynamic models, the influence of the densitydifference on traffic staibility are investigated.By incorporatingthe ITS in traffic flow, two lattice hydrodynamic modelsconsidering the difference of density are proposed to study the influence of the densitydifference between nearest lattice ahead and the current lattice on traffic flow stability.The results from the linear stability theory show that considering this density differenceand the following lattice could lead to the improvement of the traffic flow stability. Themodified Korteweg-de Vries equations (the mKdV equation, for short) near the criticalpoint are derived by using the nonlinear perturbation method to show that the traffic jamcould be described by the kink-antikink soliton solutions for the mKdV equations.Compared with those without considering the density difference, the models presentedhere improve the stability of traffic flow.The final chapter of this dissertation is devoted to a summary and prospect of furtherstudy of the road traffic flow.