On resilient control of dynamical flow networks

Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -- including structural properties, such as monotonicity, that enable tractability and scalability -- over the specific applications, connections to well-established road traffic flow models are made.Comment: accepted for publication in Annual Reviews in Control, 201

On resilient control of dynamical flow networks

Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches.In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -including structural properties, such as monotonicity, that enable tractability and scalability- over the specific applications, connections to well-established road traffic flow models are made

Urban Traffic Eco-driving: A Macroscopic Steady-State Analysis

International audienceThe problem of traveling at maximum energy efficiency (Eco-Driving) is addressed for urban traffic networks at macroscopic level. The scope of this paper is the analysis of the steady-state behavior of the system, given certain boundary flows conditions fixed by traffic lights timings, and in presence of a traffic control policy based on variable speed limits. The formal study is carried out on a two-cells variable length model adapted to the urban setup from previous works on highway traffic. Informative traffic metrics, aimed at assessing traffic and vehicles performance in terms of traveling time, infrastructure utilization and energy consumption, are then defined and adapted to the new macroscopic traffic model. If congestion in a road section does not spill back or vanish, the system is stable and many different equilibrium points can be reached via variable speed limits. Efficient operation points and traffic conditions are identified as a trade-off between optimization of global traffic energy consumption, traveling time and infrastructure utilization

Development and evaluation of advanced traveler information system (ATIS) using vehicle-to-vehicle (V2V) communication system

This research develops and evaluates an Advanced Traveler Information System (ATIS) model using a Vehicle-to-Vehicle (V2V) communication system (referred to as the GATIS-V2V model) with the off-the-shelf microscopic simulation model, VISSIM. The GATIS-V2V model is tested on notional small traffic networks (non-signalized and signalized) and a 6X6 typical urban grid network (signalized traffic network). The GATIS-V2V model consists of three key modules: vehicle communication, on-board travel time database management, and a Dynamic Route Guidance System (DRGS). In addition, the system performance has been enhanced by applying three complementary functions: Autonomous Automatic Incident Detection (AAID), a minimum sample size algorithm, and a simple driver behavior model. To select appropriate parameter ranges for the complementary functions a sensitivity analysis has been conducted. The GATIS-V2V performance has been investigated relative to three underlying system parameters: traffic flow, communication radio range, and penetration ratio of participating vehicles. Lastly, the enhanced GATIS-V2V model is compared with the centralized traffic information system. This research found that the enhanced GATIS-V2V model outperforms the basic model in terms of travel time savings and produces more consistent and robust system output under non-recurrent traffic states (i.e., traffic incident) in the simple traffic network. This research also identified that the traffic incident detection time and driver's route choice rule are the most crucial factors influencing the system performance. As expected, as traffic flow and penetration ratio increase, the system becomes more efficient, with non-participating vehicles also benefiting from the re-routing of participating vehicles. The communication radio ranges considered were found not to significantly influence system operations in the studied traffic network. Finally, it is found that the decentralized GATIS-V2V model has similar performance to the centralized model even under low flow, short radio range, and low penetration ratio cases. This implies that a dynamic infrastructure-based traffic information system could replace a fixed infrastructure-based traffic information system, allowing for considerable savings in fixed costs and ready expansion of the system off of the main network corridors.Ph.D.Committee Chair: Hunter, Michael; Committee Member: Fujimoto, Richard; Committee Member: Guensler, Randall; Committee Member: Leonard, John; Committee Member: Meyer, Michae

Multi-agent network games with applications in smart electric mobility

The growing complexity and globalization of modern society brought to light novel problems and challenges for researchers that aim to model real-life phenomena. Nowadays communities and even single individuals cannot be considered as a closed system, since one's actions create a ripple effect that ends up influencing the action of others. Therefore, the study of decision-making processes over networks became a pivotal topic in the research community. The possible applications are virtually endless and span into many different fields. Two of the most relevant examples are smart mobility and energy management in highly populated cities, where a collection of (partially) noncooperative individuals interact over a network trying to reach an efficient equilibrium point, in the sense of Nash, and share limited resources due to the environment in which they operate. In this work, we approach these problems through the lens of game theory. We use different declinations of this powerful mathematical tool to study several aspects of these themes. We design decentralized iterative algorithms solving generalized network games that generate behavioral rules for the players that, if followed, ensure global convergence. Then, we question the classical assumption of perfect players’ rationality by introducing novel dynamics to model partial rationality and analyzing their properties. We conclude by focusing on the design of optimal policies to regulate smart mobility and energy management. In this case, we create a detailed and more realistic description of the problem and use a nudging mechanism, implemented by means of a semi-decentralized algorithm, to align the users' behavior with the one desired by the policymaker

Representation of functions on big data associated with directed graphs

This paper is an extension of the previous work of Chui et al. (2015) [4], not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called digraphs, for simplicity). Besides theoretical development, this paper introduces effective mathematical tools in terms of certain data-dependent orthogonal systems for function representation and analysis directly on the digraphs. In addition, this paper also includes algorithmic development and discussion of various experimental results on such data-sets as CORA, Proposition, and Wiki-votes

Graph models of habitat mosaics

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights. © 2009 Blackwell Publishing Ltd/CNRS

Spectral graph fractional Fourier transform for directed graphs and its application

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Hermitian Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used in reducing unnecessary noise superimposed on temperature data. Finally, the performance of the proposed DGFRFT approach is also evaluated through numerical experiments using real-world directed graphs