Network Traffic Flow Evolution Based On Quantity Regulation

The aim of this dissertation is to expand the analysis method of the traditional network flow equilibrium as well as realistically and comprehensively describe the evolutionary process from the non-equilibrium state to the equilibrium state due to the perturbation of the network flow.Here,starting from the route choice behavior analysis of travelers,the influences of different route choice mechanisms of travelers on the network flow assignment under the influence of quantity signals are discussed based on the Non-Walrasian Equilibrium Theory of economics.Thus,the evolutionary process of traffic flow from the non-equilibrium state to the equilibrium state is described.The main contents and innovations are as follows.(1)Based on the Non-Walrasian Equilibrium Theory of economics,the quantity signal is introduced to the route choice process of travelers,and then the quantity equilibrium principle of network traffic flow from the non-equilibrium state to the equilibrium state is proposed.The introduction of quantity signals would result in the recasting of the route choice behavior in the process of traffic assignment.Therefore,in this dissertation,the quantity signals are quantitatively described from two perspectives of absolute quantity and relative quantity.Moreover,the influence of quantity signals on the route choice behaviors of travelers is reflected by taking the residual capacity and congestion degree as the absolute quantity and the relative quantity,respectively.(2)The route choice of travelers is simulated by the network groping process mechanism in economics.A continuous traffic flow evolution model is constructed based on the mixed adjustment of price-absolute quantity and price-relative quantity in consideration of the dual constraints of price and quantity signals.Then,the existence,uniqueness and stability of the model solution are mathematically analyzed and proved.It is suggested from the numerical simulation and parameter analysis of network that the travelers adjust between the shortest-travel-time route and the largest-residual-capacity route with regard to the price-quantity regulation route choice behavior mechanism of absolute quantity signals.Simultaneously,the travelers adjust between the shortest-travel-time route and the least-congestion-degree route in consideration of the price-quantity regulation route choice behavior mechanism of relative quantity signals.Under the double constraints of price-quantity signals of two kinds of mixed adjustment mechanisms,as the traffic demands of travelers can't be fully met,they would adjust the supply-demand relationship.Thus,they could select some uneconomical routes(i.e.long-travel-time route)with high freedom and less congestion.The proposed model can flexibly describe the dynamic evolution process of the network flow as well as objectively reflect travelers'preference for speediness and comfort in the route choice process by adjusting the influence weight of price signals and quantity signals on route choice.(3)Based on the principle of price-quantity adjustment,this dissertation takes the route congestion degree as the relative quantity signal and proposes a discrete traffic flow evolution model with the mixed price-quantity adjustment.Simultaneously,the stability of the model is mathematically proved by Brouwer's fixed point theorem and nonlinear dynamic stability theory.Taking the Nguyen-Dupuis road network as a testing example,the congestion degrees of the four most congested roads in the road network decrease by 5.8%,4%,7%,and 1.2%,respectively.The results indicate that the traffic flow evolution model under the mixed regulation mechanism of route time and route congestion can shift the flow from high-congested routes to low-congested routes.In addition,the links with low flows can attract more travelers.This conclusion reflects that travelers can continuously adjust their travel route and keep learning according to the congestion information of the road network due to the limited computing power or incomplete information.Moreover,it is shown by the improvement of congestion that some travelers choose the uneconomical(long travel time)routes due to the comfort preference or incomplete information,as well as avoid the most congested or most uncomfortable routes.This makes the overall efficiency of the road network better.Therefore,when the complete quantity signals information is provided in time or the traffic flow is reasonably adjusted by the quantity signals,the travelers with the preference of comfort or both the speediness and comfort can select the more reasonable routes.This would improve the road congestion,as well as provide new ideas for network traffic flow control,traffic induction strategies,and traffic planning.