Stochastic User Equilibrium Model With Tradable Credit Scheme And System-Wide Optimization

As a novel traffic demand management(TDM)instrument,tradable credit scheme(TCS)possessed the same powerful ability as road congestion pricing(CP)in terms of regulating traffic travel demand.Furthermore,TCS can ensure the revenue neutrality and social equity to a great extent,thus it is more acceptable for the general public than CP in the practical implemetation.Investigating the traffic network equlibrium assignment problem with TCS can not only enrich the existing traffic network equilibrium theories,but also provide a scientific guiding method for quantitatively evaluating the traffic regulation effect of TCS and designing the optimal TCS under particular management objectives.Most of the existing related researches are made based on user equilibrium(UE)model framework,with the advantages of simple modeling method and brief model expression.However,there is an unreasonable basic assumption in UE model framework that the travelers can always know the accurate travel cost of all routes.To make up for this deficiency,it is assumed that travelers have some perception errors on the route travel cost,which follow a certain random distribution,e.g.normal distribution or Gumbel distribution.Accordingly,it is necessary to investigate TCS based on the stochastic user equilibrium(SUE)model framework.Due to the great difference between SUE and UE models,the methodologies for UE model with TCS can not apply to the SUE case,hence it is necessary to carry out the special research for the various basic problems involved.Specifically,the following main contributions are made in this thesis.(1)The equivalent general SUE model with TCS and the modified Lagrangian dual method(LDM)Adding a linear TCS constraint into the traditional SUE model can not yield the equivalent SUE model with TCS.A nominal link travel time function and a path-based continuously differentiable vector function are first constructed.Then the general SUE model with TCS is established by utilizing the desirable mathematical property of the two constructed functions,and the equivalency between the proposed model and SUE condition under TCS is proved.With the assumption of Gumbel distributed perception errors,the logit-based SUE model with TCS is derived.Due to the additional linear constraint in SUE model with TCS,the classical method of succesive averages(MSA)is not applicable,thus a modified LDM is developed by analyzing the property of the dual maximization problem.The MSA is integrated in the LDM,and thus the existing program code of MSA can be nested within the LDM,hence,only the outer iteration in LDM need be focused for programming consideration.(2)The sensitivity analysis for the SUE model with TCSThe sensitivity analysis method of nonlinear programming problem does not apply to the SUE model with TCS,since its objective function contains the path-based implicit fucntion.To avoid this dilemma,the SUE conditions under TCS are refomulated as a variational inequality(VI)model with emdedding a fixed point(FP)model.By analyzing the first-order optimility condition of the VI model,the link-based equality system is obtained for the perturbation system,from which the two crucial Jacobian matrices in sensitivity analysis are derived.Then the analytical expressions of SUE link flow pattern and credit price with respect to the credit charge scheme,total credit amount and OD demands are derived by using implicit function theorem.In order to realize the application of sensitivity analysis in large scale network,the numerical calculation method for the two key Jacobian matrices is also provided.(3)The optimal TCS design problem for maximizing road network efficiencyThe upper bounds of efficiency loss for SUE under given TCS are first investigated,respectively against system optimum(SO)and stochastic system optimum(SSO).It is found that a properly designed TCS can make the efficiency loss approach zero,and the corresponding TCS are respectively SO-TCS and SSO-TCS.Since the SO-TCS does not necessarily exist under the assumption of perception errors,the necessary and sufficient condition is established for garanteeing the existence of SO-TCS,and then the linear polyhedron for SO-TCS is further provided.As for SSO-TCS,it is found that the marginal cost pricing(MCP)theory is still applicable in SSO model,which means SSO-TCS does always exist.Then the linear polyhedron for SSO-TCS is also provided.For the SSO TCS design problem with unknown travel demand function,a trial-and-error method is developed based on the link flow observation,and its convergence is proved strictly.(4)The optimal TCS design problem for maximizing road network capacityThe bi-level programming model is established for the optimal TCS design problem,with the upper level maximizing road network reserve capacity subject to link capacity constraints,and lower level being the SUE assignment problem under given TCS,in order to describe the traveler's route choice behavior under given TCS.Since the bi-level model is a NP-hard problem which is difficult to solve by using exact algorithm,thus the heuristic sensitivity analysis based(SAB)algorithm is developed.A feasibility test process is added in the SAB algorithm,which can effctively prevent erroneous interruption and ensure the feasibility of each updated solution,hence the SAB algorithm can be carried out correctly to achieve the convergence.