Stability of Intelligent Transportation Network Dynamics: A Daily Path Flow Adjustment considering Travel Time Differentiation

A theoretic formulation on how traffic time information distributed by ITS operations influences the trajectory of network flows is presented in this paper. The interactions between users and ITS operator are decomposed into three parts: (i) travel time induced path flow dynamics (PFDTT); (ii) demand induced path flow dynamics (PFDD); and (iii) predicted travel time dynamics for an origin-destination (OD) pair (PTTDOD). PFDTT describes the collective results of user’s daily route selection by pairwise comparison of path travel time provided by ITS services. The other two components, PTTDOD and PFDD, are concentrated on the evolutions of system variables which are predicted and observed, respectively, by ITS operators to act as a benchmark in guiding the target system towards an expected status faster. In addition to the delivered modelings, the stability theorem of the equilibrium solution in the sense of Lyapunov stability is also provided. A Lyapunov function is developed and employed to the proof of stability theorem to show the asymptotic behavior of the aimed system. The information of network flow dynamics plays a key role in traffic control policy-making. The evaluation of ITS-based strategies will not be reasonable without a well-established modeling of network flow evolutions

Bridging the user equilibrium and the system optimum in static traffic assignment: a review

Solving the road congestion problem is one of the most pressing issues in modern cities since it causes time wasting, pollution, higher industrial costs and huge road maintenance costs. Advances in ITS technologies and the advent of autonomous vehicles are changing mobility dramatically. They enable the implementation of a coordination mechanism, called coordinated traffic assignment, among the sat-nav devices aiming at assigning paths to drivers to eliminate congestion and to reduce the total travel time in traffic networks. Among possible congestion avoidance methods, coordinated traffic assignment is a valuable choice since it does not involve huge investments to expand the road network. Traffic assignments are traditionally devoted to two main perspectives on which the well-known Wardropian principles are inspired: the user equilibrium and the system optimum. User equilibrium is a user-driven traffic assignment in which each user chooses the most convenient path selfishly. It guarantees that fairness among users is respected since, when the equilibrium is reached, all users sharing the same origin and destination will experience the same travel time. The main drawback in a user equilibrium is that the system total travel time is not minimized and, hence, the so-called Price of Anarchy is paid. On the other hand, the system optimum is an efficient system-wide traffic assignment in which drivers are routed on the network in such a way the total travel time is minimized, but users might experience travel times that are higher than the other users travelling from the same origin to the same destination, affecting the compliance. Thus, drawbacks in implementing one of the two assignments can be overcome by hybridizing the two approaches, aiming at bridging users’ fairness to system-wide efficiency. In the last decades, a significant number of attempts have been done to bridge fairness among users and system efficiency in traffic assignments. The survey reviews the state-of-the-art of these trade-off approaches

Transportation Network Resiliency: A Study of Self-Annealing

Transportation networks, as important lifelines linking communities and goods, are indispensable for the smooth functioning of society. These networks are, however, fragile and vulnerable to natural and manmade disasters, which can disrupt their vital functionality. The role of the transportation sector becomes more crucial during disasters due to its role in pre-disaster evacuation as well as post-disaster recovery. The ability of transportation systems to retain performance during and after disasters undergoing little to no loss and their ability to return to the normal state of operation quickly after disasters defines their resilience. Authorities need to understand the degree of resilience within the transportation system under their jurisdiction and plan for improvements. In this research, attempts have been made to deal with resilience in quantitative ways to provide defensible data to decision makers to support investment strategies. Total loss in the network performance can be quantified by dealing with the variation of network performance over time after disasters and the network resilience can be measured by the ability to minimize this loss. It has been shown that robust networks retain better performance after disruptions and recovery works, which follow optimized recovery paths, in spite of constraints of resources and time, help to minimize the total losses and enhance the network resilience. The objective of this research is to create a conceptual framework to quantify resilience and discuss quantitatively the properties determining resilience of transportation networks. The concepts presented are applied to a test network to illustrate the mathematical procedures. Such methods can help decision makers analyze relative improvements in resiliency as a consequence of proposed project alternatives and help to perform benefit-cost analysis for such projects

Modeling Evacuation Risk Using a Stochastic Process Formulation of Mesoscopic Dynamic Network Loading

One of the actions usually conducted to limit exposure to a hazardous event is the evacuation of the area that is subject to the effects of the event itself. This involves modifications both to demand (a large number of users all want to move together) and to supply (the transport network may experience changes in capacity, unusable roads, etc.). In order to forecast the traffic evolution in a network during an evacuation, a natural choice is to adopt an approach based on Dynamic Traffic Assignment (DTA) models. However, such models typically give a deterministic prediction of future conditions, whereas evacuations are subject to considerable uncertainty. The aim of the present paper is to describe an evacuation approach for decision support during emergencies that directly predicts the time-evolution of the probability of evacuating users from an area, formulated within a discrete-time stochastic process modelling framework. The approach is applied to a small artificial case as well as a real-life network, where we estimate users' probabilities to reach a desired safe destination and analyze time dependent risk factors in an evacuation scenario

Mathematical Game Theory

These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in particular, combinatorial and zero-sum games as well as models for investing and betting. n-person games are studied with emphasis on notions of utilities, potentials and equilibria, which allows to subsume cooperative games as special cases. The represenation of a game theoretic system in a Hilbert space furthermore establishes a link to the mathematical model of quantum mechancis and general interaction systems

Population mobility, well-mixed clustering and disease spread: a look at COVID-19 Spread in the United States and preventive policy insights

The epidemiology of pandemics is classically viewed using geographical and political borders; however, these artificial divisions can result in a misunderstanding of the current epidemiological state within a given region. To improve upon current methods, we propose a clustering algorithm which is capable of recasting regions into well-mixed clusters such that they have a high level of interconnection while minimizing the external flow of the population towards other clusters. Moreover, we analyze and identify so called core clusters, clusters that retain their features over time (temporally stable) and independent of the presence or absence of policy measures. In order to demonstrate the capabilities of this algorithm, we use US county-level cellular mobility data to divide the country into such clusters. Herein, we show a more granular spread of SARS-CoV-2 throughout the first weeks of the pandemic. Moreover, we are able to identify areas (groups of counties) that were experiencing above average levels of transmission within a state, as well as pan-state areas (clusters overlapping more than one state) with very similar disease spread. Therefore, our method enables policymakers to make more informed decisions on the use of public health interventions within their jurisdiction, as well as guide collaboration with surrounding regions to benefit the general population in controlling the spread of communicable diseases.Comment: 18 pages, 16 figure