Routing choices in intelligent transport systems

Road congestion is a phenomenon that can often be avoided; roads become popular, travel times increase, which could be mitigated with better coordination mechanisms. The choice of route, mode of transport, and departure time all play a crucial part in controlling congestion levels. Technology, such as navigation applications, have the ability to influence these decisions and play an essential role in congestion reduction. To predict vehicles' routing behaviours, we model the system as a game with rational players. Players choose a path between origin and destination nodes in a network. Each player seeks to minimise their own journey time, often leading to inefficient equilibria with poor social welfare. Traffic congestion motivates the results in this thesis. However, the results also hold true for many other applications where congestion occurs, e.g. power grid demand. Coordinating route selection to reduce congestion constitutes a social dilemma for vehicles. In sequential social dilemmas, players' strategies need to balance their vulnerability to exploitation from their opponents and to learn to cooperate to achieve maximal payouts. We address this trade-off between mathematical safety and cooperation of strategies in social dilemmas to motivate our proposed algorithm, a safe method of achieving cooperation in social dilemmas, including route choice games. Many vehicles use navigation applications to help plan their journeys, but these provide only partial information about the routes available to them. We find a class of networks for which route information distribution cannot harm the receiver's expected travel times. Additionally, we consider a game where players always follow the route chosen by an application or where vehicle route selection is controlled by a route planner, such as autonomous vehicles. We show that having multiple route planners controlling vehicle routing leads to inefficient equilibria. We calculate the Price of Anarchy (PoA) for polynomial function travel times and show that multiagent reinforcement learning algorithms suffer from the predicted Price of Anarchy when controlling vehicle routing. Finally, we equip congestion games with waiting times at junctions to model the properties of traffic lights at intersections. Here, we show that Braess' paradox can be avoided by implementing traffic light cycles and establish the PoA for realistic waiting times. By employing intelligent traffic lights that use myopic learning, such as multi-agent reinforcement learning, we prove a natural reward function guarantees convergence to equilibrium. Moreover, we highlight the impact of multi-agent reinforcement learning traffic lights on the fairness of journey times to vehicles

Robust optimization, game theory, and variational inequalities

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 193-109).We propose a robust optimization approach to analyzing three distinct classes of problems related to the notion of equilibrium: the nominal variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand uncertainty. In the first part of the thesis, we demonstrate that the nominal VI problem is in fact a special instance of a robust constraint. Using this insight and duality-based proof techniques from robust optimization, we reformulate the VI problem over a polyhedron as a single- level (and many-times continuously differentiable) optimization problem. This reformulation applies even if the associated cost function has an asymmetric Jacobian matrix. We give sufficient conditions for the convexity of this reformulation and thereby identify a class of VIs, of which monotone affine (and possibly asymmetric) VIs are a special case, which may be solved using widely-available and commercial-grade convex optimization software. In the second part of the thesis, we propose a distribution-free model of incomplete- information games, in which the players use a robust optimization approach to contend with payoff uncertainty.(cont.) Our "robust game" model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative, distribution-free equilibrium concept, for which, in contrast to ex post equilibria, existence is guaranteed. We show that computation of "robust-optimization equilibria" is analogous to that of Nash equilibria of complete- information games. Our results cover incomplete-information games either involving or not involving private information. In the third part of the thesis, we consider uncertainty on the part of a mechanism designer. Specifically, we present a novel, robust optimization model of the network design problem (NDP) under demand uncertainty and congestion effects, and under either system- optimal or user-optimal routing. We propose a corresponding branch and bound algorithm which comprises the first constructive use of the price of anarchy concept. In addition, we characterize conditions under which the robust NDP reduces to a less computationally demanding problem, either a nominal counterpart or a single-level quadratic optimization problem. Finally, we present a novel traffic "paradox," illustrating counterintuitive behavior of changes in cost relative to changes in demand.by Michele Leslie Aghassi.Ph.D