Project Description

Public transit systems are not only essential for urban mobility but are also advantageous from the fuel consumption, pollutant emissions and traffic congestion standpoints. In addition to this, transit also provides an alternative with acceptable levels of mobility to people who cannot own or drive a car. In fact, the main goal of having a transit system is to offer good quality service, where users travel easily at a low fare while reducing pollution and traffic congestion. This goal often results in serious financial problems for the transit operators, as their revenues are rarely enough to cover their expenses, requiring subsidies funded by local governments. In this context, we propose the integration of transit and parking systems as an option to decrease the subsidies of transit systems. This integration is developed considering two different views. A physical integration of the two systems; and an integration through prices (transit fares and parking fees), where two different standpoints are considered. One that assumes a regulated market, where the parking operator revenues will be used to fund the transit operator deficits; and another that assumes a fully deregulated market, where both transit operators and parking operators have a profit maximization goal.

The physical integration of the two systems was illustrated through an optimization-based study carried out for Coimbra (Portugal), with the goal of selecting the best locations for park-and-ride facilities so that car use inside the city is minimized. Park-and-ride facilities are parking lots located in the periphery of cities to intercept car trips coming from the suburbs, and divert them to transit. In this study, the transport mode choices were assumed to be dependent on the generalized travel costs of car, transit and park-and-ride according to a logit function. The main result was that the introduction of a park-and-ride network could reduce car use in Coimbra’s city center by 19%.

The integration of transit and parking systems through prices in a regulated market was approached with an optimization model, where transit and parking are managed together to minimize the joint deficit of the respective operators, considering transit fares and parking fees as decision variables. The context of application of this model is a city divided into zones, where trips between each pair of zones can be made either by car or by bus, or not made if (generalized) travel costs are considered too high by the traveler. Modal choice in the city is described by a logit model of the generalized travel costs of both modes. In the case of car, these costs consist of vehicle depreciation, fuel, maintenance, travel time and parking fees, while time costs, discomfort costs and transit fares are the costs included in the transit generalized travel cost. This model was applied to a case study in Coimbra, where both transit and parking

systems become clearly profitable due to a substantial increase of prices. However, the relationship between demand and speed is not addressed in this model, as it is assumed that speed values remain unchanged even when modal choices change.

This shortcoming was handled by embedding on the optimization model a network level aggregate traffic model based on the macroscopic fundamental diagram (MFD), which determines the speeds and cruising-for-parking costs considering car travel demand. Due to the complexity of the optimization model, a solution method based on a traffic-equilibrium algorithm and a greedy algorithm was developed.

Through the application of a case study inspired by the city of Coimbra, it was possible to verify that the joint operating deficits were decreased, leading to a profitable transit system. An alternative SA algorithm was also developed in view of its future application to solve the previous model. If properly designed, algorithms of this type show good global optimum convergence properties. Otherwise, the quality of the best solution they return may be low or the computation time they require may be excessively long. The reason for this to happen may be because SA algorithms spend too much effort evaluating poor quality solutions. To avoid this, we hybridize a cross-entropy algorithm with a SA algorithm, in order to decrease the probability that a low-quality candidate solution is selected in each iteration. The results of a computational study developed for a facility location problem indicate that the hybrid algorithm clearly improves the classic SA algorithm.

The integration of transit and parking systems under a deregulated market was handled through a two-stage game-theoretic approach, assuming transit and parking operator as profit maximizers. The first stage decisions are parking capacity, transit frequencies and fleet size, whereas pricing decisions are made in the second stage, assuming the first-stage decisions known and fixed. The concept of subgame perfect pure strategy Nash equilibrium was used to solve this game. By analyzing several hypothetical case studies (inspired by real-world situations), it was shown how the decisions of the operators are expected to interact.

In general, the proposed models and their applications contribute what we believe to be a significant addition to the literature. These integrated transit-parking planning models provide a better understanding of how park-and-ride networks and pricing schemes affect the city’s mobility dynamics and modal choices, and insight into the impact of the decisions of transit and parking operators on their financial performance.

Research Team

CITTA

• Joana Cavadas
• António Pais Antunes (supervisor)

École Polytechnique Fédérale de Lausanne

• Nikolas Geroliminis (supervisor)

Dartmouth College

• Vikrant Vaze

Financial Support

• FCT

Stage of Progress

• Concluded in 2018