Equity-oriented skip-stopping schedule optimization in an oversaturated urban rail transit network

In this study, we focus on improving system-wide equity performance in an oversaturated urban rail transit network based on multi-commodity flow formulation. From the system perspective, an urban rail transit network is a distributed system, where a set of resources (i.e., train capacity) is shared by a number of users (i.e., passengers), and equitable individuals and groups should receive equal shares of resources. However, when oversaturation occurs in an urban rail transit network during peak hours, passengers waiting at different stations may receive varying shares of train capacity leading to the inequity problem under train all-stopping pattern. Train skip-stopping pattern is an effective operational approach, which holds back some passengers at stations and re-routes their journeys in the time dimension based on the available capacity of each train. In this study, the inequity problem in an oversaturated urban rail transit network is analyzed using a multi-commodity flow modeling framework. In detail, first, discretized states, corresponding to the number of missed trains for passengers, are constructed in a space-time-state three-dimensional network, so that the system-wide equity performance can be viewed as a distribution of all passengers in different states. Different from existing flow-based optimization models, we formulate individual passenger and train stopping pattern as commodity and network structure in the multi-commodity flow-modeling framework, respectively. Then, we aim to find an optimal commodity flow and well-designed network structure through the proposed multi-commodity flow model and simultaneously achieve the equitable distribution of all passengers and the optimal train skip-stopping pattern. To quickly solve the proposed model and find an optimal train skip-stopping pattern with preferable system-wide equity performance, the proposed linear programming model can be effectively decomposed to a least-cost sub-problem with positive arc costs for each individual passenger and a least-cost sub-problem with negative arc costs for each individual train under a Lagrangian relaxation framework. For application and implementation, the proposed train skip-stopping optimization model is applied to a simple case and a real-world case based on Batong Line in the Beijing Subway Network. The simple case demonstrates that our proposed Lagrangian relaxation framework can obtain the approximate optimal solution with a small-gap lower bound and a lot of computing time saved compared with CPLEX solver. The real-world case based on Batong Line in the Beijing Subway Network compares the equity and efficiency indices under the operational approach of train skip-stopping pattern with those under the train all-stopping pattern to state the advantage of the train skip-stopping operational approach.     

A justice-theoretic approach to the distribution of transportation benefits: Implications for transportation planning practice in the United States

Transportation improvements inevitably lead to an uneven distribution of user benefits, in space and by network type (private and public transport). This paper makes a moral argument for what would be a fair distribution of these benefits. The argument follows Walzer’s “Spheres of Justice” approach to define the benefits of transportation, access, as a sphere deserving a separate, non-market driven, distribution. That distribution, we propose, is one where the maximum gap between the lowest and highest accessibility, both by mode and in space, should be limited, while attempting to maximize average access. We then review transportation planning practice for a priori distributional goals and find little explicit guidance in conventional and even justice-oriented transportation planning and analyses. We end with a discussion of the implications for practice.     

Managing bottleneck congestion with tradable credits

We demonstrate the efficiency and effectiveness of a tradable credit system in managing the morning commute congestion with identical and nonidentical commuters. The credit system consists of a time-varying credit charged at the bottleneck and an initial credit distribution to the commuters, where the credits are universal in terms of time. Credits are tradable between the commuters and the credit price is determined by a competitive market. Under the assumption that late-arrival is not allowed, we prove that an optimal credit charging scheme, which completely eliminates the bottleneck queue, always exists despite how commuters vary in their value-of-time (VOT). The optimal charge rate is strictly increasing and convex with time, which therefore drives the commuters to depart in the increasing order of their VOT. The optimal credit charging scheme is pareto-improving, but may cause undesirable welfare distribution among the commuters. Our study shows that a combination of an initial credit distribution and an optimal credit charging scheme can simultaneously achieve system optimum and certain forms of equality (e.g., “numerical” or “proportional” equality), and that the commuters in the middle VOT bracket will receive the most credits under the proportionally equitable credit distribution.     

城市轨道交通投资的公平性及其影响因素分析

城市轨道交通是建设成本与运营费用昂贵的社会公共基础设施,作为一种稀缺资源,应体现投资的公平性原则,实现普遍服务和持续发展的目标。阐述城市轨道交通投资公平性的内涵与特点,分析了城市轨道交通投资的公平性的影响因素,包括：交通功能的发挥、开发利益还原以及弱势群体权益的保障,并提出了政府在城市轨道交通规划、开发利益还原制度、票价政策、公众参与机制方面保证投资公平性的基本思路。