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

Wealth Inequality and the Price of Anarchy

The price of anarchy quantifies the degradation of social welfare in games due to the lack of a centralized authority that can enforce the optimal outcome. It is known that, in certain games, such effects can be ameliorated via tolls or taxes. This leads to a natural, but largely unexplored, question: what is the effect of such transfers on social inequality? We study this question in nonatomic congestion games, arguably one of the most thoroughly studied settings from the perspective of the price of anarchy. We introduce a new model that incorporates the income distribution of the population and captures the income elasticity of travel time (i.e., how does loss of time translate to lost income). This allows us to argue about the equality of wealth distribution both before and after employing a mechanism. We establish that, under reasonable assumptions, tolls always increase inequality in symmetric congestion games under any reasonable metric of inequality such as the Gini index. We introduce the inequity index, a novel measure for quantifying the magnitude of these forces towards a more unbalanced wealth distribution and show it has good normative properties (robustness to scaling of income, no-regret learning). We analyze inequity both in theoretical settings (Pigou\u27s network under various wealth distributions) as well as experimental ones (based on a large scale field experiment in Singapore). Finally, we provide an algorithm for computing optimal tolls for any point of the trade-off of relative importance of efficiency and equality. We conclude with a discussion of our findings in the context of theories of justice as developed in contemporary social sciences and present several directions for future research

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy

Architectures and algorithms for dynamic overlay networks

Most of today’s Internet of Things (IoT) applications assume that data will be moved offdevices into centralized cloud platforms. While existing IoT systems leverage cloud-based analytics for meaningful data reasoning, the assumption that data should always be moved off the devices is problematic. The amount of data to be moved from devices over Internet gateways to cloud platforms is huge which potentially make it cost inefficient. In other scenarios, privacy concerns of customers or organizational rules complicate the process of transferring data to third-party data centers.This dissertation proposes architectures and dynamic overlay network algorithms for in-networkand edge processing of data offered by the globally available IoT devices and provides a global platform for meaningful and responsive data analysis and decision making. The proposed techniques shift IoT analytics from a ”collect data now and analyze it later” scenario to directlyproviding meaningful information from the in-network processing of devices data at or near thedevices. The techniques serve future IoT use cases including distributed context awareness, on-demand data analysis, and in-network decision making. The dissertation comprises three main components.The first component is a device management protocol for cloning devices’ data in proximateEdge Computing platforms. Unlike existing application-layer IoT management protocols theproposed protocol uses the LTE LTE-A radio frame structure, device-to-device communication,and IoT data properties to avoid excessive network access latency in existing technologies.The second component realizes distributed IoT analytics as overlay networks of devices clones. By means of virtual network embedding, it selects and interconnects devices’ clones to efficiently realize applications’ virtual topologies to achieve goals such as minimum latency, minimum infrastructure cost, or maximum infrastructure utilization.Finally, the dissertation presents a communication middleware that allows autonomous discovery, self-deployment, and online migration of devices’ clones across heterogeneous Edge computing platforms. The middleware ensures that communication latency between clones is kept minimum despite the uncontrolled variability of the network and hosting platforms conditions.We evaluate the proposed architectures and algorithms through simulations and prototypeimplementation of various components in controlled testbed environments, which we evaluateusing real user applications. We explore the feasibility of the proposed techniques from boththeoretical and practical perspectives.Keywords: Cloud Computing, Internet of Things, Algorithmic Game Theory, Compressive Sensin

How to Route and Tax Selfish Unsplittable Traffic

We study the problem of assigning unsplittable traffic to a set of m links so to minimize the maximum link congestion (i.e., the makespan). We consider the case of selfish agents owning pieces of the traffic. In particular, we introduce a variant of the model by Koutsopias and Papadimitriou [1999] in which owners of the traffic cannot directly choose which link to use; instead, the assignment is performed by a scheduler. The agents can manipulate the scheduler by reporting falseinformation regarding the size of each piece of unsplittable traffic.We provide upper and ower bounds on the approximation achievable by mechanisms that induce a Nash equilibrium when all agents report their true values.For the case of each agent owning one job, our positive results for m identical links show the effectiveness of introducing such a scheduler since, in this case, (1+ε)-approximate solutions are guaranteed in polynomial time. In contrast, the result by Koutsopias and Papadimitriou [1999] shows that, without payments and allowing selfish routing, Nash equilibria yield (in the worst case) Ω(log m over log log m)-approximate solutions, even for unitary weighted traffic. When links have different speeds we prove lower and upper bounds on the approximation achievable by a mechanism inducing a Nash equilibrium.Similar approximability results for identical machines have been achieved by Feldman et al. [2003]. However these results do not hold in our setting because their model assumes that the algorithm is provided with the correct traffic weights. For the case of agents owning more than one job, we give mechanisms that achieve constant approximation and prove lower bounds on the approximation ratio that can be achieved by a mechanism

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

How to Route and Tax Selfish Unsplittable Traffic

We study the problem of assigning unsplittable traffic to a set of $m$ links so to minimize the maximum link congestion (i.e., the makespan). We consider the case of *selfish agents* owning pieces of the traffic. In particular, we introduce a variant of the model by Koutsoupias and Papadimitriou [1999] in which owners of the traffic cannot directly choose which link to use; instead, the assignment is performed by a *scheduler*. The agents can manipulate the scheduler by reporting false information regarding the size of each piece of unsplittable traffic. We provide upper and lower bounds on the approximation achievable by *mechanisms* that induce a Nash equilibrium when all agents report their true values. For the case of each agent owning one job, our positive results for $m$ identical links show the effectiveness of introducing such a scheduler since, in this case, (1+\epsilon)-approximate solutions are guaranteed in polynomial time. In contrast, the result by Koutsoupias and Papadimitriou [1999] shows that, without payments and allowing selfish routing, Nash equilibria yield (in the worst case) $\Omega(\frac{\log m}{\log \log m})$-approximate solutions, even for unitary weighted traffic. When links have different speeds we prove lower and upper bounds on the approximation achievable by a mechanism inducing a Nash equilibrium. For the case of agents owning more than one job, we give mechanisms that achieve constant approximation and prove lower bounds on the approximation ratio that can be achieved by a mechanism

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum