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

Stability analysis on a dynamical model of route choice in a connected vehicle environment

Research on connected vehicle environment has been growing rapidly to investigate the effects of real-time exchange of kinetic information between vehicles and road condition information from the infrastructure through radio communication technologies. A fully connected vehicle environment can substantially reduce the latency in response caused by human perception-reaction time with the prospect of improving both safety and comfort. This study presents a dynamical model of route choice under a connected vehicle environment. We analyze the stability of headways by perturbing various factors in the microscopic traffic flow model and traffic flow dynamics in the car-following model and dynamical model of route choice. The advantage of this approach is that it complements the macroscopic traffic assignment model of route choice with microscopic elements that represent the important features of connected vehicles. The gaps between cars can be decreased and stabilized even in the presence of perturbations caused by incidents. The reduction in gaps will be helpful to optimize the traffic flow dynamics more easily with safe and stable conditions. The results show that the dynamics under the connected vehicle environment have equilibria. The approach presented in this study will be helpful to identify the important properties of a connected vehicle environment and to evaluate its benefits

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

Detection and optimization problems with applications in smart cities

This dissertation proposes solutions to a selected set of detection and optimization problems, whose applications are focused on transportation systems. The goal is to help build smarter and more efficient transportation systems, hence smarter cities. Problems with dynamics evolving in two different time-scales are considered: (1) In a fast time-scale, the dissertation considers the problem of detection, especially statistical anomaly detection in real-time. From a theoretical perspective and under Markovian assumptions, novel threshold estimators are derived for the widely used Hoeffding test. This results in a test with a much better ability to control false alarms while maintaining a high detection rate. From a practical perspective, the improved test is applied to detecting non-typical traffic jams in the Boston road network using real traffic data reported by the Waze smartphone navigation application. The detection results can alert the drivers to reroute so as to avoid the corresponding areas and provide the most urgent "targets" to the Transportation department and/or emergency services to intervene and remedy the underlying cause resulting in these jams, thus, improving transportation systems and contributing to the smart city agenda. (2) In a slower time-scale, the dissertation investigates a host of optimization problems, including estimation and adjustment of Origin-Destination (OD) demand, traffic assignment, recovery of travel cost functions, and joint recovery of travel cost functions and OD demand (joint problem). Integrating these problems leads to a data-driven predictive model which serves to diagnose/control/optimize the transportation network. To ensure good accuracy of the predictive model and increase its robustness and consistency, several novel formulations for the travel cost function recovery problem and the joint problem are proposed. A data-driven framework is proposed to evaluate the Price-of-Anarchy (PoA; a metric assessing the degree of congestion under selfish user-centric routing vs. socially-optimal system-centric routing). For the case where the PoA is larger than expected, three viable strategies are proposed to reduce it. To demonstrate the effectiveness and efficiency of the proposed approaches, case-studies are conducted on three benchmark transportation networks using synthetic data and an actual road network (from Eastern Massachusetts (EMA)) using real traffic data. Moreover, to facilitate research in the transportation community, the largest highway subnetwork of EMA has been released as a new benchmark network

Mathematical programming algorithms for equilibrium road traffic assignment

The equilibrium approach to representing interactions between the supply and demand sides of traffic assignment has been used widely in the estimation of traffic flows on road networks. Although this approach is quite reasonable, there is a considerable gap between the observed and modelled values of cost and flow. This gap can be reduced by relaxing some of the restrictive assumptions behind the models used in order to enhance their realism. This study investigates the solutions of various advanced road traffic assignment models. Priority and signal controlled junctions are modelled in traffic assignment in order to enhance the realism of junction analysis. A multiclass assignment is modelled to represent different groups of users. These problems are known to be non-separable because traffic cannot be segmented in such a way that the costs incurred by any one segment vary only with the flow within that segment. Existence, uniqueness and stability properties of solutions to these problems are investigated. These analyses are important to know the reliability and repeatability of any solutions that are calculated. Analyses of these properties lead to some guidelines for using these detailed models. A number of new solution algorithms are developed to solve the resulting traffic assignment problems. These algorithms belong to the general category of simplicial decomposition which solves the problem by dividing it into two subproblems: a linear and a master subproblem which are solved alternately. One of the advantages of these algorithms is that they operate in a lower dimensional space than that of original feasible region and hence allow large-scale problems to be solved with improved accuracy and speed of convergence. These improved algorithms give many choices to the traffic management studies. Two substantial networks have been used to compare the performance of new algorithms on the various models developed. They have performed favourably by comparison with existing algorithms. A small example network has been used to investigate existence, uniqueness and stability properties using the models. In a priority controlled model, a unique stable solution has been obtained using the model whilst in a signal controlled model, multiple and unstable solutions have been obtained. In a multiclass model, a unique solution has been obtained in terms of the total class flow whilst multiple solutions have been obtained in terms of each class flow. These results correspond well to the theoretical analyses of these models, which has shown to have indeterminate behaviour and by the nature of these models assumed, the degree of non-separability is ordered according to priority controlled, multiclass and signal controlled models