109 results found
Wang Y, Liu H, Han K, et al., 2015, Day-to-Day Congestion Pricing and Network Resilience, Transportmetrica A: Transport Science, Vol: 11, Pages: 873-895, ISSN: 2324-9943
One important indicator of traffic network resilience is rapidity, which measures the speed at which a system returns to its normal state after a disruption. In this paper, we propose a day-to-day tolling scheme to increase the rapidity of road traffic systems after disturbances caused by natural or man-made events such as accidents, flooding, earthquake, and infrastructure damage. The theory of projected dynamical systems is applied to model the transient behaviour of traffic when faced with network disruptions. We further provide three computationally tractable solution methods for designing the toll under various assumptions on the information availability. The effectiveness of the proposed tolling scheme is guaranteed by theoretically established estimates. Numerical experiments on several test networks demonstrate the effectiveness of the dynamic tolling mechanisms in improving the rapidity and the potential cost efficiency of the traffic systems.
Liu H, Han K, Gayah VV, et al., 2015, Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control, Transportation Research Part C: Emerging Technologies, Vol: 59, Pages: 260-277, ISSN: 0968-090X
Han K, Szeto WY, Friesz TL, 2015, Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance, Transportation Research Part B: Methodological, Vol: 79, Pages: 16-49, ISSN: 0191-2615
Han K, Piccoli B, Szeto WY, 2015, Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness, Transportmetrica B-Transport Dynamics, Vol: 4, Pages: 187-222, ISSN: 2168-0566
We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traf- fic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton-Jacobi equation and junction models defined via the notions of demand and supply. We show that the proposed LKWM can be formulated as a system of differential algebraic equations (DAEs), which captures shock formation and propagation, as well as queue spillback. The DAE system, as we show in this paper, is the continuous-time counterpart of the link transmission model. In addition, we present a solution existence theory for the continuous-time network model and investigate continuous dependence of the solution on the initial data, a property known as well-posedness. We test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.
Liu H, Han K, Gayah V, et al., 2015, Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control, 21st International Symposium on Transportation and Traffic Theory, Pages: 536-555
We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is then solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data- driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic.
Han K, Gayah VV, 2015, Continuum signalized junction model for dynamic traffic networks: Offset, spillback, and multiple signal phases, Transportation Research Part B: Methodological, Vol: 77, Pages: 213-239, ISSN: 0191-2615
Han K, Liu H, Gayah V, et al., 2015, A robust optimization approach for dynamic traffic signal control with emission considerations, Transportation Research Part C - Emerging Technologies, Vol: 70, Pages: 3-26, ISSN: 0968-090X
We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive.To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.
Han K, Sun Y, Liu H, et al., 2015, A bi-level model of dynamic traffic signal control with continuum approximation, Transportation Research Part C - Emerging Technologies, Vol: 55, Pages: 409-431, ISSN: 0968-090X
This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.
Piccoli B, Han K, Friesz TL, et al., 2015, Second-order models and traffic data from mobile sensors, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 32-56, ISSN: 0968-090X
Piccoli B, Han K, Friesz TL, et al., 2015, Second-order models and traffic data from mobile sensors, Transportation Research Part C: Emerging Technologies, Vol: 52, Pages: 32-56, ISSN: 0968-090X
Szeto WY, Wang Y, Han K, 2015, Bounded Rationality in Dynamic Traffic Assignment, Bounded Rational Choice Behaviour, Applications in Transport, Editors: Rasouli, Timmermans, Publisher: Emerald Group Publishing, ISBN: 9781784410711
Purpose -- This chapter explores a descriptive theory of multidimensional travel agent-based microsimulation.Theory -- A descriptive theory on multidimensional travel behaviour is conceptualised. It theorizes multidimensional knowledge updating, search start/stopping criteria and search/decision heuristics. These components are formulated or empirically modelled and integrated in a unified and coherent approach.Findings -- The theory is supported by empirical observations and the derived quantitative models are tested by an agent-based simulation on a demonstration network.Originality and value -- Based on artificially intelligent agents, learning and search theory and bounded rationality, this chapter makes an effort to embed a sound theoretical foundation for the computational process approach and agent-based micro-simulations. A pertinent new theory is proposed with experimental observations and estimations to demonstrate agents with systematic deviations from the rationality paradigm. Procedural and multidimensional decision-making are modelled. The numerical experiment highlights the capabilities of the proposed theory in estimating rich behavioural dynamics.
Shang W, Pien KC, Han K, et al., 2015, Robustness and Topology Analysis of European Air Traffic Network Using Complex Network Theory, The 94th Transportation Research Board Annual Meeting
This paper explores topological and operational features of the European Air Traffic Network (EATN), which consists of airports and Area Control Centres (ACCs), with the goal of analysing and quantifying network robustness. The EATN is regarded as a directed, weighted and asymmetric graph, where various metrics, including betweenness, are studied and analysed statistically. On the operational side, the EATN is recognized as a flow-bearing and capacitated air transport network with established origins and destinations as well as flight routes. We propose a Relative Area Index (RAI), combined with network flow maximization techniques, to capture and quantify the degradation in the network throughput in the event of local disruptions on different levels-a concept frequently referred to as robustness in the literature. Our findings show that the RAI follows the power law distribution. Moreover, it is not correlated with betweenness centrality, which is a popular index used to infer the robustness of topological networks. We show that topological inferences such as betweenness are insufficient to capture network robustness in the real world, and that a class of new indices that reflect the operational constraints, flow patterns and behavioural assumptions should be developed to assess the robustness of air traffic networks.
Mascia M, Hu SJ, Han K, et al., 2015, Reducing Environmental Impact By Adaptive Traffic Control And Management For Urban Road Networks, The 94th Transportation Research Board Annual Meeting, Publisher: Transportation Research Board
This paper investigates the effectiveness of traffic signal control and variable message sign (VMS) as environmental traffic management tool. The focus is on black carbon and CO2, which are among the highest contributors to climate change. The modelling tool chain adopted to support this study includes traffic microsimulation, emission modelling and dispersion modelling. A number of scenarios have been simulated with different levels of demand and VMS compliance rates. The results demonstrate the potential of these interventions in reducing black carbon and CO2 emissions and improving air quality, as well as reducing traffic congestion and travel delays.
Hu J, Mascia M, Han K, et al., 2015, Assessment of different urban traffic control strategy impacts on vehicle emissions, The 47th Annual UTSG Conference
This paper investigates the influence of traffic signal control strategy on vehicle emissions, vehicle journey time and total throughput flow within a single isolated four-armed junction. Two pre-timed signal plans are considered, one with two-stages involving permissive-only opposing turns and the other with four-stages which has no conflicting traffic. Additionally, the increase in efficiency by utilising actuated signal timing where green time is re-optimised as flow values vary is investigated. A microscopic traffic simulation model is used to model flows and AIRE (Analysis of Instantaneous Road Emissions) microscopic emissions model is utilised to out- put emission levels from the flow data. A simple junction model shows that the two-stage signal plan is more efficient in both emis- sions and journey time. However, as the level of opposed turning vehicles and conflicting movement increases, the two-stage model moves to being the inferior signal plan choice and the four-stage plan outputs fewer emissions than the two-stage plan. A real-world example of a four-armed junction has been used in this study and from the traffic survey data and existing junction layout; it is rec- ommended that a two-stage plan is used as it produces lower amounts of emissions and shorter journey times compared to a four-stage plan. The results also show that nitrogen oxides (NOx) are the most sensitive to changes in flow followed by carbon dioxide (CO2), Black Carbon and then particulate matter (PM10).
, 2015, A framework for the classification and prioritization of arrival and departure routes in multi-airport systems terminal manoeuvring areas
© 2015 American Institute of Aeronautics and Astronautics Inc, AIAA. All right reserved. Typically major cities (London, New York, Tokyo) are served by several airports effectively creating a Multi-Airport System or Metroplex. The operations of the Metroplex airports are highly dependent on one another, which renders their efficient management difficult. This paper proposes a framework for the prioritization of arrival and departure routes in Multi-Airport Systems Terminal Manoeuvring Areas. The framework consists of three components. The first component presents a new procedure for clustering arrival and departure flights into dynamic routes based on their temporal and spatial distributions through the identification of the important traffic flow patterns throughout the day of operations. The second component is a novel Analytic Hierarchy Process model for the prioritization of the dynamic routes, accounting for a set of quantitative and qualitative characteristics important for Multi-Airport Systems operations. The third component is a priority-based model for the facility location of the optimal terminal waypoints (fixes), which accounts for the derived priorities of each dynamic route, while meeting the required separation distances. The proposed Analytic Hierarchy Process model characteristics are validated by subject matter experts. The developed framework is applied to the London Metroplex case study.
Han K, Lascia M, North R, et al., 2015, Day-to-day dynamic traffic assignment model with variable message signs and endogenous user compliance
This paper proposes a dual-time-scale, day-to-day dynamic traffic assignmentmodel that takes into account variable message signs (VMS) and its interactionswith drivers' travel choices and adaptive learning processes. The within-daydynamic is captured by a dynamic network loading problem with en route updateof path choices influenced by the VMS; the day-to-day dynamic is captured by asimultaneous route-and-departure-time adjustment process that employs boundeduser rationality. Moreover, we describe the evolution of the VMS compliancerate by modeling drivers' learning processes. We endogenize traffic dynamics,route and departure time choices, travel delays, and VMS compliance, andthereby captur their interactions and interdependencies in a holistic manner. Acase study in the west end of Glasgow is carried out to understand the impactof VMS has on road congestion and route choices in both the short and long run.Our main findings include an adverse effect of the VMS on the networkperformance in the long run (the 'rebound' effect), and existence of anequilibrium state where both traffic and VMS compliance are stabilized.
Simon H, Margherita M, Martin L, et al., 2014, Field Investigation of Vehicle Acceleration at the Stop Line with a Dynamic Vision Sensor, Journal of Traffic and Transportation Engineering, Vol: 2, ISSN: 2328-2142
Mascia M, Hu SJ, Han K, et al., 2014, Environmental impact of combined ITS traffic management strategies, The 20th International Transport and Air Pollution Conference 2014
Transport was responsible for 20% of the total greenhouse gas emissions in Europe during 2011(European Environmental Agency 2013) with road transport being the key contributor. To tacklethis, targets have been established in Europe and worldwide to curb transport emissions. Thisposes a significant challenge on Local Government and transport operators who need to identifya set of effective measures to reduce the environmental impact of road transport and at the sametime keep the traffic smooth. Of the road transport pollutants, this paper considers NOx, CO2 andblack carbon (BC). A particular focus is put on black carbon, which is formed through incompletecombustion of carboneous materials, as it has a significant impact on the Earth’s climate system.It absorbs solar radiation, influences cloud processes, and alters the melting of snow and icecover (Bond et al. 2013). BC also causes serious health concerns: black carbon is associatedwith asthma and other respiratory problems, heart attacks and lung cancer (Sharma 2010; UnitedStates Environmental Protection Agency 2012).Since BC emissions are mainly produced during the decelerating and accelerating phases(Zhang et al. 2009), ITS actions able to reduce stop&go phases have the potential to reduce BCemissions. This paper investigates the effectiveness of combined ITS actions in urban context inreducing CO2 and BC emissions and improving traffic conditions.
Han K, Friesz TL, Yao T, et al., 2014, Formulation, existence, and computation of simultaneous route-and-departure choice boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance, 5th International Symposium on Dynamic Traffic Assignment
This paper analyzes the continuous-time simultaneous route-and-departure choice (SRDC) dy- namic user equilibrium (DUE) that incorporates boundedness of user rationality. As such, the boundedly rational dynamic user equilibrium (BR-DUE) model assumes that travelers do not always seek the least costly route-and-departure-time choice. Rather, their perception of travel cost is affected by an indifference band which describes travelers’ tolerance towards the differ- ence between their experienced travel costs and the minimum travel cost. We further extend our subject of investigation to include a variable tolerance (VT) BR-DUE with endogenously deter- mined tolerances that may depend not only on a particular path, but also on the established path flows (path departure rates). The VT-BR-DUE model captures more realistic driving behaviors that stem from path heterogeneity, and drivers’ observations of prevailing traffic conditions.For the first time in the literature, the continuous-time VT-BR-DUE problem, together with the BR-DUE problem as a special case, is formulated as an infinite dimensional variational in- equality, a differential variational inequality, and a fixed point problem. Existence results for VT- BR-DUE and BR-DUE are provided based on assumptions weaker than those made for SRDC DUEs. Moreover, we propose, based on the fixed point formulation, a fixed-point iterative al- gorithm that computes VT-BR-DUE and BR-DUE in continuous time, which is then tested on several networks in terms of solution characteristics, convergence, and computational time.
Han K, Friesz TL, Yao T, 2014, Vehicle spillback on dynamic traffic networks and what it means for dynamic traffic assignment models, 5th International Symposium on Dynamic Traffic Assignment
This paper investigates the vehicle spillback phenomenon and its impact on network modeling and dynamic traffic assignment (DTA). We first present two analytical formulations of the continuous-time dynamic net- work loading (DNL) problem, as a system of partial differential algebraic equations (PDAEs) and a system of differential algebraic equations (DAEs) respectively. Derivation of these two systems is based on the Lighthill- Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956) with vehicle spillback explicitly captured. The DAE system also employs a variational method known as the Lax-Hopf formula. Conditions that trigger vehicle spillback are explicitly identified and mathematically analyzed. Moreover, it is demonstrated that vehicle spillback has a number of quantitative and qualitative effects on the path delay operator essential to DTA modeling. Notably, we provide an example that shows the discontinuity of the path delay operator in the presence of spillback in a DNL procedure. Such discontinuity persists when certain discrete-time models, such as the cell transmission model (Daganzo, 1995a) and the link transmission model (Yperman et al., 2005) are employed. Such finding reveals several difficulties in the existence proof and computation for certain DTA models when queue spillback is captured by the underlying network performance model.
Pien KC, Majumdar A, Han K, et al., 2014, A linear programming approach to maximum flow estimation on the European air traffic network, 6th International Conference on Research in Air Transportation
A linear programming (LP) approach is proposed toestimate the maximum flow in the European air traffic network,based on empirical traffic data and capacity constraints atairports and in Area Control Centres. In order to validate themodel and the associated results, we treat historical datacollected on 1 July 2012 as the empirical maximum flow andcompare them with the theoretical maximum established by theLP model. The results show that the proposed model, despite itsrelatively simple structure and assumptions, has captured theoverall congestion status and the saturated state of the network,which is verified statistically. Meanwhile, we utilize data on AirTraffic Flow Management (ATFM) delays to validate a queuingmodel by comparing the empirical data with predicted dataobtained from Little’s theorem. The ATFM delays, whencombined with the proposed LP model, suggest a viable way ofidentifying and quantifying several capacity factors that impacton network capacity such as airspace availability and ATFM.Future work will describe and predict more accurately the airtraffic network in Europe.
Han K, Sun Y, Liu H, et al., A bi-level model of dynamic traffic signal control with continuum approximation, 5th International Symposium on Dynamic Traffic Assignment
Han K, Friesz TL, Yao T, 2014, A variational approach for continuous supply chain networks, SIAM Journal on Control and Optimization, Vol: 52, Pages: 663-686, ISSN: 0363-0129
We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896–920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433–460] and [D. Armbruster, C. De Beer, M. Fre- itag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104–114]. A model was proposed for such a network by [S. G ̈ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559] using a system of coupling ordinary differential equations and partial differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, a computational algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIPs). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones [A. Fu ̈genschuh, S. Go ̈ttlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490–1507; S. Go ̈ttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559], which demonstrates the modeling and computational advantages of the variational approach.
Han K, Gayah V, Piccoli B, et al., 2014, On the continuum approximation of the on-and-off signal control on dynamic traffic networks, Transportation Research Part B - Methodological, Vol: 61, Pages: 73-97
In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. While accurate, the use of binary variables can cause problems when studying large networks with many intersections. Instead, the signal control can be approximated through a continuum approach where the on-and-off control variable is replaced by a continuous priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment.Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach; i.e., to what extent is this a valid approximation for the on-and-off case. The goal of this paper is to answer these basic research questions and provide further guidance for the application of such continuum signal model. In particular, by employing the Lighthill-Whitham-Richards model (Lighthill and Whitham, 1955; Richards, 1956) on a traffic network, we investigate the convergence of the on-and-off signal model to the continuum model in regimes of diminishing signal cycles. We also provide numerical analyses on the continuum approximation error when the signal cycles are not infinitesimal. As we explain, such convergence results and error estimates depend on the type of fundamental diagram assumed and whether or not vehicle spillback occurs to the signalized intersection in question. Finally, a traffic signal optimization problem is presented and solved which illustrates the unique advantages of applying the continuum signal model instead of the on-and-off model.
Han K, Piccoli B, Gayah V, et al., 2014, On the continuum approximation of the on-and-off signal control for dynamic networks, Transportation Research Board 93rd Annual Meeting
In the modeling of signalized junctions, a signal control is typically expressed as an on-and-off control in continuous time, or as a binary variable in discrete time. One way of approximating such signal control is through a continuum approach where the on-and-off control variable is replaced by a priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment.Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach; to what extent is this a valid approximation. The goal of this paper is to answer these basic research questions and provide guidance for application, by rigorously analyzing a network model consistent with the Lighthill-Whitham-Richards model (Lighthill and Whitham, 1955; Richards, 1956). In particular, convergence of the on-and-off signal model to the continuum model is investigated in regimes of diminishing signal cycles. We also provide numerical analysis on the approximation error when the signal cycle is not infinitesimal. The convergence results and approximation accuracy are dependent on the type of fundamental diagram employed and whether or not spillback occurs in a network.
Piccoli B, Han K, Friesz TL, et al., 2014, Second-order models and traffic data from mobile sensors, Transportation Research Board 93rd Annual Meeting
Mobile sensing enabled by on-board GPS or smart phones has become the primary source of traffic data. For sufficient coverage of the traffic stream, it is important to main- tain a reasonable penetration rate of probe vehicles. From the standpoint of estimating higher-order traffic quantities such as acceleration/deceleration, emission rate and fuel consumption rate, it is desirable to examine the effectiveness of the sampling frequency of current sensing technology in capturing these higher-order variations inherent in the traffic stream. Of the two concerns raised above, the latter is rarely studied in the literature.In this paper, we study the two concerns of mobile sensing: penetration rate and sam- pling frequency, and their impacts on the quality of traffic estimation. A computational method is proposed that integrates vehicle trajectory data into a second-order hydrody- namic model known as the phase transition model (Colombo, 2002a). Moreover, we utilize the Next Generation SIMulation (NGSIM, 2006) dataset containing high time-resolution vehicle trajectories. It is demonstrate through extensive numerical study that while first-order traffic quantities can be accurately estimated using the prevailing sampling frequency at a reasonably low penetration rate, higher-order traffic quantities tend to be misinter- preted due to insufficient sampling frequency of current mobile devices. We propose, for estimating emission and fuel consumption rates, a correction factor approach which is proven to yield improved accuracy via statistical validation.
Jin PJ, Han K, Ran B, 2014, Some theoretical and practical perspectives of the travel time kine- matic wave model: Generalized solution, applications, and limitations, Transportation Research Board 93rd Annual Meeting
This paper explores the travel time kinematic wave (KW) model recently-reveal through Hamilton-Jacobi (H-J) Partial Differential Equation (PDE) theory proposed by Laval and Leclercq. We focus on theoretical and practical aspects of the travel time KW model in real-world traveler information and traffic management applications. The travel time kinematic wave (KW) model is an equivalent representation of the Lighthill-Whitham- Richards (LWR) model. The model preserves both the spatial representation in Euler model and the numerical and formulation benefits in Lagrangian model, making it suitable for conducting traffic state estimation based on prevailing mobile sensor data such as GPS, cellular, and Bluetooth probe data. In this paper, we provide an in-depth discussion on the physical meaning of the model revealed through a heuristic derivation of the travel time KW model and the rigorous proof of its requivalenso to the other two Euler and Lagrangian model. We extend the Lax-Hopf formulations and solution methods proposed in Laval and Leclercq’s study to account for internal boundary problems that may be used to formulating signalized intersection, active traffic management, and the emerging connected vehicle data. Meanwhile, by comparing the two Lagrangian formulations of LWR with respect to vehicle sinks and sources, route-based, and lane-based applications, we attempt to provide a realistic perspective on the potentials and challenges facing Lagrangian traffic flow models.
Bressan A, Han K, 2013, Existence of optima and equilibria for traffic flow on networks, Networks and Heterogeneous Media, Vol: 8, Pages: 627-648, ISSN: 1556-1801
Han K, 2013, An Analytical Approach to Sustainable Transportation Network Design
This dissertation emphasizes the modeling and computation of multi-agent, dynamic, interdependent, complex and competitive transportation systems, by invoking mathematically canonical and tractable forms. Applications of such work focuses on the design and management of a transportation network, which include not only problems of adding/removing capacity by changing nodes and arc sets, but also the determination of piecewise smooth decision variables like prices, tolls, traffic signals, information accessibility, and other control variables associated with Stackelberg mechanisms and so-called second-best strategies. The primary modeling paradigms employed by this dissertation are differential Nash-like games and differential Stackelberg games that are constrained by systems of (partial) differential algebraic equations. Such modeling paradigms capture several key elements of modern traffic networks including travel choices, demand evolution, vehicular flow propagation, as well as their economic, social and environmental impacts. The model of simultaneous route-and-departure choice dynamic network user equilibrium developed in the early 1990s has been extended in this dissertation to incorporate elastic travel demands and bounded rationality. The invocation of infinite-dimensional variational inequality and differential variational inequality formulations of Nash-like differential game allows existence, uniqueness, computability, stability and other qualitative properties of these models to be addressed and answered. A critical component of the Nash-like network congestion game is the so-called dynamic network loading (DNL) sub-problem, which aims at describing and predicting the spatial-temporal evolution of traffic flows on a network that is consistent with established route and departure time choices of travelers. Several traffic flow models, including the Lighthill-Whitham-Richards network model accommodating vehicle spillback, have been analyzed in depth along w
Han K, Friesz TL, Yao T, 2013, Existence of simultaneous route and departure choice dynamic user equilibrium, Transportation Research Part B: Methodological, Vol: 53, Pages: 17-30, ISSN: 0191-2615
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