Research On Congestion Management Models Based On Equilibrium Theory And Optimization Algorithms

With the rapid development of the economy and the acceleration of urbanization,traffic congestion has become an increasingly serious problem in whole large cities.How to effectively alleviate congestion is always a hot research topic in academia.Traffic demand management is an effective way to alleviate traffic congestion,which is according to control the traffic flow to balance the supply and demand of the traffic network.Road charging and tradable credit scheme are the two main means used in traffic demand management.The main purpose of them is to balance the flow of each route in the road network by levying additional expenses for the users,so that the whole network can reach the system optimum state.In this paper,based on the traffic network in different situations,some concrete traffic congestion management schemes are proposed.Then,by analyzing the route choosing behavior of the travelers,the corresponding variational inequality model or minimization model is established based on equilibrium theory,and some optimization algorithms are proposed.These models and methods can provide theoretical and programmatic references for government and traffic managers.Firstly,aiming at the traffic flow assignment problem under capacity constraints,we propose a variational inequality model based on user equilibrium theory by analyzing the travel behavior of travellers.Combined with the optimization theory,the existence and uniqueness of the solution are analyzed.We further propose a symmetric alternating direction method with logarithmic quadratic proximal(LQP)penalty to solve the proposed model.Each iteration of the proposed method contains two updates of the dual multiplier,and the maximal step size range theoretically is obtained to guarantee the convergence of the method.The introduced LQP penalty can transform the constrained optimization subproblem into an unconstrained optimization one,which can improve the efficiency of the method.Numerical experiments are conducted on a traffic network to verify the effectiveness and superiority of the method,and the equilibrium link flow pattern is obtained.The proposed model and solving method contribute to the traffic flow prediction and provide reference for the government and traffic managers to issue policies.Then,to alleviate traffic congestion,based on the user heterogeneity,we propose to implement both toll and tradable credit scheme for the public-private partnership transportation network,i.e.,tolling and charging tradable credits for the users who use the government-built public roads and BOT private roads.Based on the travelers' routing behavior under this mixed strategy,we build the variational inequality model of user equilibrium and market equilibrium.Then,according to the system optimum model,the mixed strategy set can be obtained that promotes the user equilibrium flow pattern to the system optimal flow pattern,and the upper bound of system efficiency loss under mixed strategy is also derived.Furthermore,we propose two bi-level programming models covering other objectives and obtain the optimal mixed strategy.Finally,a numerical experiment on a specific road network is conducted,which can obtain the specific amount of tradable credits and charging value for each public road and BOT private road respectively,and the total number of windows for that need to be set in the network.Next,in response to the call of green traveling,a multi-modal transportation network with new energy vehicles is considered,and a mixed strategy,which contains a tolling scheme for conventional vehicles and a tradable credit scheme for new energy vehicles,is proposed.Since the credits are issued free by the government in each period,tradable credit scheme can be seen as subsidizing the new energy vehicles while easing traffic congestion.Under this mixed strategy,based on users' travel behavior and equilibrium theory,a mixed equilibrium-based variational inequality model including user equilibrium and Cournot-Nash equilibrium is established,and the properties of the model are analyzed with the help of optimization theory.In order to characterize the buying and selling behavior in the credit trading market,applying the loss aversion theory,the paper further explores the effects of transaction costs in the credit market on the equilibrium link-flow patterns.Finally,aiming at the problem of dynamic congestion management which considers the path selection and departure time simultaneously in the traffic network,we propose a variational inequality model based on the dynamic user equilibrium theory by analyzing the travel behavior,and the equivalent models are discussed.Then,a fast projection gradient algorithm with relaxation and extrapolation is proposed for solving this model.Each iteration of the proposed algorithm contains a relaxation sub-step and an extrapolation sub-step,which are extremely inexpensive but can effectively improve the efficiency.Meanwhile,the convergence results of the algorithm are given.In addition,by some numerical experiments on several practical large-scale traffic networks,the effectiveness of the algorithm is verified,and the equilibrium link-flow patterns on different paths at different time are obtained.In conclusion,traffic demand management is an effective way to alleviate traffic congestion.It is feasible to ease traffic congestion through implementing the tolling and tradable credit schemes.Based on the equilibrium theory,the congestion management models and corresponding optimization algorithms in different scenarios are proposed,which further enriches the theory of traffic congestion management and expands the applications of the tolling and tradable credit schemes.