Congestion Pricing Design On General Transportation Network:Models And Algorithms

Recent several years, with the fast development of urbanization and the rapid in-creasement of traffic demand, traffic congestion has become a serious social problem and been a main threat to sustainable urban transportation system. It is widely recognized that congestion pricing is an efficient way to alleviate this problem. After imposing a suitable toll on road users, path and link flow and even traffic demand can be affected so as to obtain more efficient utilization of existing road infrastructures. Playing an economic role for market-oriented demand management, congestion pricing has received much attention and been deeply investigated both academically and practically.First, we investigate the optimal time-based toll design problem for cordon-based congestion pricing scheme on the general transportation network with movement pro-hibitions and speed limits, in which toll charges are determined according to time con-sumed by travelers in traversing a predetermined cordon. Under the common hypoth-esis of travelers following the deterministic user equilibrium principle, this practical time-based toll design problem is formulated as a mathematical programming with e-quilibrium constraint (MPEC) model, and solved by the Hooke-Jeeves algorithm, a derivative-free pattern search method. Taking into account the movement prohibitions at intersections, this paper presents a shortest path model with movement prohibitions and develops an efficient branch and bound algorithm. Subsequently, the deterministic user equilibrium model can be solved via combining the proposed branch and bound algorithm with method of successive averages (MSA). Finally, a medium-sized network example is adopted to numerically validate the proposed models and algorithms, and further analyzes and discusses different features and results of four kinds of toll design schemes.Second, we investigate the length-based and congestion-based C-logit stochastic us-er equilibrium (SUE) and second-best congestion pricing problems on a bimodal trans-portation network with road and rail travel modes. The C-logit model captures the overlapping effect among the different paths via two versions of commonality factors, sequentially it has ability to obtain a more realistic traffic flow distribution pattern. Re-defining the link travel cost functions and employing a binary logit model for the mode-split, the bimodal C-logit SUE models can be substantially simplified:the length-based model is transformed into an unconstrained nonlinear mathematical programming for-mulation and the congestion-based model is equivalent to a variational inequality (Ⅵ) formulation. Such models are verified to satisfy the bimodal C-logit SUE conditions at their stationary points and can be solved by existing algorithms. Taking each bi-modal C-logit SUE model as a constraint, the second-best congestion pricing problem is thus formulated as two bi-level programming models, which can be solved by the pro-posed bi-objective penalty function algorithm which is more efficient and augmented Lagrangian multiplier method, respectively. A small-sized numerical example is pre-sented to investigate the impact of second-best pricing scheme on the mode-split and equilibrium flow distribution on the bimodal network, and a medium-sized network is adopted to illustrate the efficiencies of the bi-objective penalty function method.Third, we presents a multi-class reliability-based user equilibrium model with e-lastic demand for the degradable transportation network. Due to the uncertainties of path travel time induced by random capacity degradation, the model captures travel-ers’path choice behaviors in form of robust effective path travel time and is no need of known travel time probability distribution. Involving travelers’ heterogeneous degrees of risk-aversion, the equilibrium model can be transformed into an equivalent variation-al inequality (Ⅵ) problem. A heuristic solution algorithm is proposed for solving the Ⅵ problem. Taking the Ⅵ model as a constraint, a multi-class reliability-based robust congestion pricing model is formulated as a mathematical programming with equilibri-um constraints (MPEC) problem, which can be solved by the sensitivity analysis-based conjugate sub-gradient projection method. Two numerical examples are provided to illustrate the applications of the presented models and efficiencies of the solution algo-rithms.Finally, we design and analyze an alternative tradable travel credit scheme on the general transportation network for managing travelers’ route choice behaviors.The scheme is a kind of charging and rewarding mechanism, which provides an attempt to urge travelers to plan their travel routes reasonably so that excessive traffic congestion can be mitigated. Mobility credits are imposed on those travelers who use high con-gested routes, while rewarded credits are given to those travelers who switch to the low congested routes.A free tradable market is created such that the travelers paying credits can purchase them from those earning them from the rewarding travel route choices. When the total amount of credits earned is equal to the amount of credits con-sumed, transfer of wealth can only take place among the travelers and hence overcome the inequity problem of congestion pricing. On the general transportation network, the type of tradable credit schemes can be formulated as a mathematical programming with equilibrium constraint (MPEC) model.Based on the model, a credit charging mecha-nism under the system optimum and Pareto-Improving system optimum conditions is obtained.