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This paper examines the design of the credit-based congestion management schemes that achieve Pareto-improving outcome in general two-mode networks. It is assumed that transit is a slower but cheaper alternative to driving alone. The distributional welfare effects of congestion pricing on users with the different value of time (VOT) in Liu and Nie (Trans Res Board 2283:34–43, 2012) are used in developing Pareto-improving credit schemes. We show that, similar to the single-mode model, the sufficient and necessary condition for the existence of a discriminatory Pareto-improving credit scheme is the reduction in the total system cost. A sufficient condition for the existence of an anonymous Pareto-improving credit scheme is also derived. A cross-OD subsidization scheme is proposed when the sufficient condition is not satisfied for each origin-destination (O-D) pair. Numerical experiments on the expanded Sioux Falls networks with a log-normal VOT distribution demonstrate that the proposed Pareto-improving scheme can generate positive net revenue in the presence of good transit coverage. more...

This paper is concerned with the problem of finding optimal sub-routes from a set of predefined candidate transit routes with the objectives of maximizing transit ridership as well as minimizing operational costs. The main contributions of this paper are: (1) considering transit ridership maximization in a multi-objective bi-level optimization framework; (2) proposing a greedy algorithm for the multi-objective design problem; (3) applying an efficient path-based algorithm to solve the lower level multi-modal traffic assignment problem. Numerical experiments indicate that the proposed algorithm is not only able to approximate the Pareto-optimal solutions with satisfactory accuracy, but also achieves a fast performance even for problems of real-world scale. more...

This paper aims to incorporate two important measures into a freight shortest path problem, namely reliability and sustainability. Reliability measure deals with the uncertainty of link travel time while sustainability measure tends to reduce the fuel consumption and emission along the path. Greenhouse gas (GHG) emission rates are generated from Motor Vehicle Emission Simulator (MOVES) model and approximated as a function of the average link travel speed. To model uncertainty, the link travel speed is treated as a discrete random variable with a given distribution. Freight carriers are assumed to be risk-averse; for example, given two paths with the same average cost, carriers prefer the one with less variability. The risk-averse behavior is captured by the second order stochastic dominance (SSD) relationship. Specifically, SSD constraints are introduced in our model to narrow down the feasible paths which dominate a chosen benchmark path. The reliable and sustainable routing model is formulated as an integer program that can be easily tailored to a variety of modeling preferences. The study experiments with eight variants of the base model, each corresponding to a different trade-off strategy between three objectives, namely, efficiency, reliability and sustainability. The numerical experiments illustrate the benefits of the models discussed in the paper. more...

This paper seeks to apply a new tradable credit scheme in the morning commute problem. When implementing such a scheme, the congestion management authority first delineates a peak-time window and then requires all traveler who pass the bottleneck within that window to either pay certain units of mobility credits, or a peak time toll (which is comparably more expensive). The authority also rewards credits to anyone who passes the bottleneck during the designated off-peak time window. An artificial market is created so that the travelers may trade these credits with each other. Our analyses, which are based on the Vickrey’s bottleneck model managed by step tolls, indicate that the proposed scheme has several notable advantages. First, the market allows those who value travel time savings less to be directly compensated by selling credits to those who value them more. This mechanism promises simpler and fairer distribution of the benefits from congestion relief. Second, as no transfer of wealth takes places between travelers and the authority, the payment made to acquire credits is less likely to be perceived as a tax. Third, the rewarding-charging mechanism avoids the top-down allocation of credits in existing tradable credit schemes. In the proposed scheme, credits are only rewarded to those who contribute to congestion relief. Last but not least, the proposed scheme is easy to understand and simple to implement. In particular, we show that the best choice of the rewarding-charging ratio is 1, i.e., each peak-time user will be charged one credit and each off-peak user will be awarded one credit. more...

This paper studies optimal path problems integrated with the concept of second order stochastic dominance. These problems arise from applications where travelers are concerned with the trade off between the risks associated with random travel time and other travel costs. Risk-averse behavior is embedded by requiring the random travel times on the optimal paths to stochastically dominate that on a benchmark path in the second order. A general linear operating cost is introduced to combine link- and path-based costs. The latter, which is the focus of the paper, is employed to address schedule costs pertinent to late and early arrival. An equivalent integer program to the problem is constructed by transforming the stochastic dominance constraint into a finite number of linear constraints. The problem is solved using both off-the-shelf solvers and specialized algorithms based on dynamic programming (DP). Although neither approach ensures satisfactory performance for general large-scale problems, the numerical experiments indicate that the DP-based approach provides a computationally feasible option to solve medium-size instances (networks with several thousand links) when correlations among random link travel times can be ignored. more...

The problem of estimating origin-destination travel demands from partial observations of traffic conditions has often been formulated as a network design problem (NDP) with a bi-level structure. The upper level problem in such a formulation minimizes a distance metric between measured and estimated traffic conditions, and the lower level enforces user-equilibrium traffic conditions in the network. Since bi-level problems are usually challenging to solve numerically, especially for large-scale networks, we proposed, in an earlier effort (Nie et al., Transp Res, 39B:497–518, 2005), a decoupling scheme that transforms the O–D estimation problem into a single-level optimization problem. In this paper, a novel formulation is proposed to relax the user equilibrium conditions while taking users’ route choice behavior into account. This relaxation approach allows the development of efficient solution procedures that can handle large-scale problems, and makes the integration of other inputs, such as path travel times and historical O–Ds rather straightforward. An algorithm based on column generation is devised to solve the relaxed formulation and its convergence is proved. Using a benchmark example, we compare the estimation results obtained from bi-level, decoupled and relaxed formulations, and conduct various sensitivity analysis. A large example is also provided to illustrate the efficiency of the relaxation method. more...

This paper studies the dynamic user optimal (DUO) traffic assignment problem considering simultaneous route and departure time choice. The DUO problem is formulated as a discrete variational inequality (DVI), with an embeded LWR-consistent mesoscopic dynamic network loading (DNL) model to encapsulate traffic dynamics. The presented DNL model is capable of capturing realistic traffic phenomena such as queue spillback. Various VI solution algorithms, particularly those based on feasible directions and a line search, are applied to solve the formulated DUO problem. Two examples are constructed to check equilibrium solutions obtained from numerical algorithms, to compare the performance of the algorithms, and to study the impacts of traffic interacts across multiple links on equilibrium solutions. more...

Optimal path problems are important in many science and engineering fields. Performance criteria may vary in coping with uncertainty, such as expectation, reliability, value at risk, etc. In this paper, we will first summarize our recent work on a dynamic programming based optimal path algorithm for maximizing the time reliability. We then study the convergence properties of the algorithm by introducing two special successive approximation sequences. Finally we will show the connection between the maximum reliability problem and the shortest and k-shortest path problems. more...