The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.

The role of initial credit distribution scheme (ICDS) in managing network mobility has long been overlooked in previous studies of tradable credit scheme (TCS), which may make their results disputable in the reality, as the travelers possessing leftover credits can get some subsidy from the credit market and offset part of travel cost. In this paper, the disequilibrium phenomenon of previous user equilibrium (UE) solution is shown when traveler’s cognitive illusion (CI) is considered. Then, a new UE condition with TCS is defined with the ICDS and CI explicitly considered. To comprehensively reveal the impacts of ICDS on UE solution, four different types of ICDS are introduced and analyzed in a unified variational inequality (VI) modeling framework. The uniqueness of the UE link flow and market equilibrium (ME) credit price is also investigated. Furthermore, the mathematical program with equilibrium constraint (MPEC) for the optimal ICDS design problem is established, with the optimization objective being maximizing network reserve capacity. A modified relaxation algorithm is adopted to solve the MPEC. The numerical example shows that a properly designed ICDS can not only improve the network reserve capacity, but also decrease the travel cost of all the travelers in the network simultaneously.

In this paper, the generalized SUE and credit market equilibrium (ME) conditions are firstly presented, and a novel equivalent linearly-constrained minimization model is established. Due to the specialty of the proposed model, the conventional solution algorithm, such as method of successive average (MSA) can’t be applied. In order to develop an efficient solution algorithm, the Lagrangian dual formulation of the proposed model is analyzed. We find that the Lagrangian dual formulation is a continuously differentiable concave maximization problem sharing the same optimal solution with the original model, and that its gradient can be obtained by invoking MSA. According to these two desirable properties, a convergent solution algorithm is developed, of which the outer iteration is implemented by using gradient projection method with a predetermined step size sequence while the inner iteration is implemented by using MSA. Finally, a numerical example is presented to illustrate the proposed model and algorithm.

A tradable credit scheme (TCS) is a novel traffic demand management (TDM) measure that can effectively mitigate traffic congestion in a revenue-neutral way. Under a given TCS, the cognitive illusion (CI) would occur when travelers instinctively use a specious thinking logic to estimate travel cost. The traveler’s CI would significantly influence his/her route choice behaviors, and thus the regulation effect of TCS on mitigating traffic congestion. To reveal the impacts of implementation policies of TCS on managing network mobility in the context of the traveler’s CI, this study investigated the traffic equilibrium assignment model with consideration of the traveler’s CI and the specific implementation policies of TCS. By incorporating the two types of factors into the generalized path travel cost (GPTC), the coupled user equilibrium (UE) and market equilibrium (ME) conditions are established to describe the equilibrium state of the traffic network under a given TCS. As the implementation policies of TCS are factored in the GPTC, different types of initial credit distribution scheme (ICDS) and the transaction costs (TC) of trading credits can be analyzed within the unified model framework. The coupled UE and ME conditions are then reformulated as an equivalent variational inequality (VI) model, and the sufficient conditions for the uniqueness of UE link flows and ME credit price are also provided. The system optimal (SO) TCS design problem is further investigated to achieve the minimum total travel time (TTT) of the transportation network, and two analytical methods are proposed to obtain the SO TCS in the context of the traveler’s CI. Numerical experiments are presented to verify the proposed model and methods. The results show that the presence of the traveler’s CI has an effect of lowering the ME credit price, and ICDS and TC have a complex network-wide influence on the ME credit price and UE link flows, which depends on the specific values of the relevant parameters.

This paper investigates the optimal road toll design problem from the perspective of sustainable development at network-wide level. In this paper the sustainable development level of transportation system is quantitatively described with the total vehicular emission, total fuel consumption, and total travel time in the network. In order to simultaneously consider the impacts of all these three indicators on sustainability of transportation system, we integrate them into a sustainable development index (SD-index) by a linear combination, and then we establish the corresponding bilevel optimization model. The upper level problem is the network toll design problem to maximize the SD-index from the viewpoint of traffic managers, and the lower level problem is to depict travelers’ route choice behavior under a certain road toll scheme. Finally, a combined genetic algorithm and gradient projection algorithm (GA-GP) is used to solve the bilevel model, in which the GP algorithm solves the traffic assignment problem with road toll scheme in the lower level. In order to verify the proposed model and algorithm, we take the Nguyen-Dupuis network for the numerical example, and the computing results show that the model and algorithm are effective and efficient.