Modeling real-world processes as convex optimization or variational inequality problems is a common practice as it enables to leverage powerful Read More Register
Modeling real-world processes as convex optimization or variational inequality problems is a common practice as it enables to leverage powerful mathematical tools for the study of such processes. For example, in transportation science, the selfish behavior of agents (from shorted path routing) leads to an aggregate cost in the network worse than the system’s optimum, and which can be analytically quantified. In the first part of our work, we briefly review the selfish routing game, which is a popular game-theoretical framework to model the urban transportation network. As an application, we study the impact of the increasing penetration of routing apps on road usage. Its conclusions apply both to manned vehicles in which human drivers follow app directions, and unmanned vehicles following shortest path algorithms. We show that the increased usage of GPS routing provides a lot of benefits, such as decrease in average travel times and total vehicle miles traveled. However, this global increased efficiency in urban mobility has negative impacts as well, which are not addressed by the scientific community: increase in traffic in cities bordering highway from users taking local routes to avoid congestion. In the second part, we present a statistical framework for the fitting of equilibrium models based on measurements of states in equilibrium using the empirical risk minimization principle, which consists in choosing the fit giving the lowest expected loss under the empirical measure. For the class of models of interest, we derive bounds on the prediction error of the model. In the third part, we propose two novel frameworks for traffic estimation, which is necessary for empirical minimization. In the first framework, we focus on estimating the traffic state on highways, modeled as switching dynamical system, with a state space partitioned into an exponential number of polyhedra in which one mode is active. We propose a feasible approach based on the interactive multiple model (IMM), and apply the k-means algorithm on historical data to partition modes into clusters, thus reducing the number of modes. In the second traffic estimation framework, we develop a convex optimization methodology for the route flow estimation problem from the fusion of vehicle count and cellular network data.