A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation

Improving the performance of a traffic system by fair rerouting of travelers

Some traffic management measures route drivers towards socially-desired paths in order to achieve the system optimum: the traffic state with minimum total travel time. In previous attempts, the behavioral response to route advice is often not accounted for since some drivers are advised to take significantly longer paths for the system’s benefit. Hence, these drivers may not comply with such advice and the optimal state will not be achieved. In this paper, we propose a social routing strategy to approach the optimal state while accounting for fairness in the resulting state. This routing strategy asks travelers to take a limited detour in order to improve efficiency. We show that the best possible paths (in terms of efficiency) to be proposed by a service adopting this strategy can be found by solving a bilevel optimization problem with a non-unique lower-level solution. We use techniques from parametric analysis to show that the directional derivative of the lower-level link flows however exists. This derivative is the optimal solution of a quadratic optimization problem with a suitable route flow solution as parameter. We use the derivative in a descent algorithm to solve the bilevel problem. Numerical experiments in a realistic environment show that the routing strategy only asks a small fraction of the drivers to take a limited detour and thereby substantially improves the performance of the traffic system

Online Resource Inference in Network Utility Maximization Problems

The amount of transmitted data in computer networks is expected to grow considerably in the future, putting more and more pressure on the network infrastructures. In order to guarantee a good service, it then becomes fundamental to use the network resources efficiently. Network Utility Maximization (NUM) provides a framework to optimize the rate allocation when network resources are limited. Unfortunately, in the scenario where the amount of available resources is not known a priori, classical NUM solving methods do not offer a viable solution. To overcome this limitation we design an overlay rate allocation scheme that attempts to infer the actual amount of available network resources while coordinating the users rate allocation. Due to the general and complex model assumed for the congestion measurements, a passive learning of the available resources would not lead to satisfying performance. The coordination scheme must then perform active learning in order to speed up the resources estimation and quickly increase the system performance. By adopting an optimal learning formulation we are able to balance the tradeoff between an accurate estimation, and an effective resources exploitation in order to maximize the long term quality of the service delivered to the users

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

Security and Energy Efficiency in Resource-Constrained Wireless Multi-hop Networks

In recent decades, there has been a huge improvement and interest from the research community in wireless multi-hop networks. Such networks have widespread applications in civil, commercial and military applications. Paradigms of this type of networks that are critical for many aspects of human lives are mobile ad-hoc networks, sensor networks, which are used for monitoring buildings and large agricultural areas, and vehicular networks with applications in traffic monitoring and regulation. Internet of Things (IoT) is also envisioned as a multi-hop network consisting of small interconnected devices, called ``things", such as smart meters, smart traffic lights, thermostats etc. Wireless multi-hop networks suffer from resource constraints, because all the devices have limited battery, computational power and memory. Battery level of these devices should be preserved in order to ensure reliability and communication across the network. In addition, these devices are not a priori designed to defend against sophisticated adversaries, which may be deployed across the network in order to disrupt network operation. In addition, the distributed nature of this type of networks introduces another limitation to protocol performance in the presence of adversaries. Hence, the inherit nature of this type of networks poses severe limitations on designing and optimizing protocols and network operations. In this dissertation, we focus on proposing novel techniques for designing more resilient protocols to attackers and more energy efficient protocols. In the first part of the dissertation, we investigate the scenario of multiple adversaries deployed across the network, which reduce significantly the network performance. We adopt a component-based and a cross-layer view of network protocols to make protocols secure and resilient to attacks and to utilize our techniques across existing network protocols. We use the notion of trust between network entities to propose lightweight defense mechanisms, which also satisfy performance requirements. Using cryptographic primitives in our network scenario can introduce significant computational overhead. In addition, behavioral aspects of entities are not captured by cryptographic primitives. Hence, trust metrics provide an efficient security metric in these scenarios, which can be utilized to introduce lightweight defense mechanisms applicable to deployed network protocols. In the second part of the dissertation, we focus on energy efficiency considerations in this type of networks. Our motivation for this work is to extend network lifetime, but at the same time maintain critical performance requirements. We propose a distributed sleep management framework for heterogeneous machine-to-machine networks and two novel energy efficient metrics. This framework and the routing metrics are integrated into existing routing protocols for machine-to-machine networks. We demonstrate the efficiency of our approach in terms of increasing network lifetime and maintaining packet delivery ratio. Furthermore, we propose a novel multi-metric energy efficient routing protocol for dynamic networks (i.e. mobile ad-hoc networks) and illustrate its performance in terms of network lifetime. Finally, we investigate the energy-aware sensor coverage problem and we propose a novel game theoretic approach to capture the tradeoff between sensor coverage efficiency and energy consumption

Intelligent and High-Performance Behavior Design of Autonomous Systems via Learning, Optimization and Control

Nowadays, great societal demands have rapidly boosted the development of autonomous systems that densely interact with humans in many application domains, from manufacturing to transportation and from workplaces to daily lives. The shift from isolated working environments to human-dominated space requires autonomous systems to be empowered to handle not only environmental uncertainties such as external vibrations but also interaction uncertainties arising from human behavior which is in nature probabilistic, causal but not strictly rational, internally hierarchical and socially compliant.This dissertation is concerned with the design of intelligent and high-performance behavior of such autonomous systems, leveraging the strength from control, optimization, learning, and cognitive science. The work consists of two parts. In Part I, the problem of high-level hybrid human-machine behavior design is addressed. The goal is to achieve safe, efficient and human-like interaction with people. A framework based on the theory of mind, utility theories and imitation learning is proposed to efficiently represent and learn the complicated behavior of humans. Built upon that, machine behaviors at three different levels - the perceptual level, the reasoning level, and the action level - are designed via imitation learning, optimization, and online adaptation, allowing the system to interpret, reason and behave as human, particularly when a variety of uncertainties exist. Applications to autonomous driving are considered throughout Part I. Part II is concerned with the design of high-performance low-level individual machine behavior in the presence of model uncertainties and external disturbances. Advanced control laws based on adaptation, iterative learning and the internal structures of uncertainties/disturbances are developed to assure that the high-level interactive behaviors can be reliably executed. Applications on robot manipulators and high-precision motion systems are discussed in this part