Research On The Evolution Of Network Traffic Flow Based On Disequilibrium Theory

The key to constructing the evolution model of network traffic flow is to assume that traveler chooses travel routes according to what kind of behavior criterion.The disequilibrium theory indicates that there is little possibility that supply and demand will be equal in all markets at all times totally depending on price regulation.The doers can not only obtain the price signal in the market,but more importantly,they can obtain quantity signal.Thus,the doers are subject to the double constraints of price and quantity in the market.In this paper,the path-travel time is regarded as price to describe the driving time on the current optional routes,the path-residual capacity is regarded as quantity to describe the vehicle flow on the current optional routes,and divides traveler's route choice behavior into three classes based on disequilibrium theory,one full compliance with the travel time on the optional routes,another full compliance with the residual capacity on the optional routes,and the third comprehensive consideration for the travel time and residual capacity on the optional routes.Next,the research on the evolution of network traffic flow will focus on these three classes of route choice behaviors.(1)The principle of price regulation user equilibrium with minimum path-travel time is proposed.The evolution model of network traffic flow under price regulation and its solution algorithm are established,and the existence,uniqueness,and stability of the solution to the model are proved.Through numerical example,the impact of system parameter and price on the evolution results of network traffic flow are analyzed.It is found that the change of system parameter may affect the convergence rate of the evolutionary trajectory of network traffic flow under price regulation,the evolution result of network traffic flow under price regulation conforms to the classical Wardrop user equilibrium,and each path flow can be converged to stable state after a period of fluctuation.(2)The principle of quantity regulation user equilibrium with minimum maximum path-residual capacity is proposed.The evolution model of network traffic flow under quantity regulation is established,the solution algorithm of the model is given,and the existence,uniqueness,and stability of the solution to the model are proved.Through different scale test road network,the impact of quantity on the distribution and dynamic evolution of network traffic flow are analyzed.The results show that each path flow can be converged to stable state after a period of fluctuation,and the stable state corresponds to the quantity regulation user equilibrium flow pattern.(3)The principle of price-quantity regulation user equilibrium with the comprehensive minimum of path-travel time and path-residual capacity.The evolution model of network traffic flow under price-quantity regulation is established,the solution algorithm of the model is given,and the existence,uniqueness,and stability of the solution to the model are proved.Through numerical experiments,the evolution processes of network traffic flow under different regulation modes are analyzed.The results show that the evolution model of network traffic flow under price-quantity regulation can simulate the process of path flow varying with time.The evolution result of price-quantity regulation is a mixed equilibrium of price regulation user equilibrium and quantity regulation user equilibrium,which can simulate the evolution process of multi-class network traffic flow.(4)Suppose that traveler's route choice behavior follows the principle of price-quantity user equilibrium,a day-to-day stochastic evolution model of network traffic flow under price-quantity regulation is established based on the stochastic user equilibrium model,and the solution algorithm of the model is given.Using the variational inequalities and nonlinear dynamical stability theorems,it is proved that the day-to-day stochastic evolution model of network traffic flow under price-quantity regulation has a unique solution,and the unique solution is asymptotically stable under certain conditions.At last,taking a test road network as example,three day-to-day stochastic evolution models of network traffic flow under single price regulation,single quantity regulation and price-quantity regulation are calculated and analyzed,respectively.The results show that each path flow in these three models can be converged to stable state after a finite travel adjustment,the single price regulation and single quantity regulation are the special case of the day-to-day stochastic evolution model of network traffic flow under price-quantity regulation,and the day-to-day stochastic evolution model of network traffic flow under price-quantity regulation can simulate the impact of heterogeneous travel behavior on the distribution and dynamic evolution of network traffic flow.