109 results found
Han K, Friesz TL, Liu H, et al., 2013, Dynamic congestion and tolls with mobile source emission, The 20th International Symposium on Transportation and Traffic Theory (ISTTT2013)
This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical programming with equilibrium constraints (MPEC) problem and then reformulated as mathematical programming with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty- based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.
Friesz TL, Han K, Meimand A, et al., 2013, Network User Equilibrium with Elastic Demand: Formulation, Qualitative Analysis and Computation
In this paper we present a differential variational inequality formulation ofdynamic network user equilibrium with elastic travel demand. We discuss itsqualitative properties and provide algorithms for and examples of its solution.
Friesz TL, Han K, Liu H, et al., 2013, Dynamic Congestion and Tolls with Mobile Source Emission, Procedia - Social and Behavioral Sciences, Vol: 80, Pages: 818-836, ISSN: 1877-0428
Han K, Friesz TL, Yao T, 2013, A partial differential equation formulation of Vickrey’s bottleneck model, part II: Numerical analysis and computation, Transportation Research Part B: Methodological, Vol: 49, Pages: 75-93, ISSN: 0191-2615
Han K, Friesz TL, Yao T, 2013, A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis, Transportation Research Part B: Methodological, Vol: 49, Pages: 55-74, ISSN: 0191-2615
Han K, Friesz TL, Yao T, 2013, A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control
This paper is concerned with adaptive signal control problems on a roadnetwork, using a link-based kinematic wave model (Han et al., 2012). Such amodel employs the Lighthill-Whitham-Richards model with a triangularfundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) isapplied so that the system dynamics can be determined without knowledge of thetraffic state in the interior of each link. A Riemann problem for thesignalized junction is explicitly solved; and an optimization problem isformulated in continuous-time with the aid of binary variables. Atime-discretization turns the optimization problem into a mixed integer linearprogram (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang,2004; Lo, 1999b), the proposed framework does not require modeling orcomputation within a link, thus reducing the number of (binary) variables andcomputational effort. The proposed model is free of vehicle-holding problems, and capturesimportant features of signalized networks such as physical queue, spill back,vehicle turning, time-varying flow patterns and dynamic signal timing plans.The MILP can be efficiently solved with standard optimization software.
Han K, Yao T, Friesz TL, 2013, Lagrangian-based Hydrodynamic Model: Freeway Traffic Estimation
This paper is concerned with highway traffic estimation using traffic sensingdata, in a Lagrangian-based modeling framework. We consider theLighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards,1956) in Lagrangian-coordinates, and provide rigorous mathematical resultsregarding the equivalence of viscosity solutions to the Hamilton-Jacobiequations in Eulerian and Lagrangian coordinates. We derive closed-formsolutions to the Lagrangian-based Hamilton-Jacobi equation using the Lax-Hopfformula (Daganzo, 2005; Aubin et al., 2008), and discuss issues of fusingtraffic data of various types into the Lagrangian-based H-J equation. Anumerical study of the Mobile Century field experiment (Herrera et al., 2009)demonstrates the unique modeling features and insights provided by theLagrangian-based approach.
Piccoli B, Han K, Friesz TL, et al., 2013, Estimating Fuel Consumption and Emissions via Traffic Data from Mobile Sensors, 51st IEEE Annual Allerton Conference on Communication, Control, and Computing, Publisher: IEEE, Pages: 472-477, ISSN: 2474-0195
Bressan A, Han K, Rampazzo F, 2013, On the control of non holonomic systems by active constraints, Discrete and Continuous Dynamical Systems, Vol: 33, Pages: 3329-3353, ISSN: 1078-0947
Friesz TL, Han K, Neto PA, et al., 2013, Dynamic user equilibrium based on a hydrodynamic model, Transportation Research Part B: Methodological, Vol: 47, Pages: 102-126, ISSN: 0191-2615
Friesz TL, Han K, 2013, Dynamic Network User Equilibrium, Publisher: Springer
Bressan A, Han K, 2012, Nash equilibria for a model of traffic flow with several groups of drivers, ESAIM: Control, Optimisation and Calculus of Variations, Vol: 18, Pages: 969-986, ISSN: 1292-8119
Han K, Hu H, Ko E, et al., 2012, A variational approach to modeling aircraft hoses and flexible conduits, Mathematics-in-Industriy Case Studies, Vol: 4, Pages: 1-13, ISSN: 1913-4967
Airplanes have thousands of hoses and flexible conduits in con- junction with moving parts, and it is essential that the conduits do not tangle or kink and that the minimal amount of material is used to minimize weight. To prevent the necessity of building plywood prototypes and arranging hoses by trial and error, the simulation of the resting states of the conduits serves as a tool for design. Here, we model the resting state of a conduit as being a critical point of the elastic energy functional – the integral of the square curvature – in neglecting gravity, torsion, and shape memory. Using a varia- tional approach, we find the Euler-Lagrange equations for the critical point of the energy functional. We use a robust, parametric representation for the centerline of the conduit in three dimensional space and consider both free length and constrained length problems using the Lagrangian multiplier method. The ultimate goal towards which we step with this work is to, with a bottoms-up approach, use large-scale simulations in the design of the positions and slopes of the fittings of and lengths of conduits used in aircraft construction. This problem was brought by The Boeing Company to a student modeling camp at the Institute for Mathematics and its Applications in 2011, and this paper describes the solution found by the student team.
Han K, Friesz TL, Yao T, 2012, Explicit solution to Vickrey’s model in continuous-time with application to DTA, The 4th International Symposium on Dynamic Traffic Assignment
Han K, Friesz TL, Yao T, 2012, Existence and properties of state operators in DUE models, The 4th International Symposium on Dynamic Traffic Assignment
In this paper, we establish and prove analytical properties of the state operator embedded in an optimal control problem, in the context of dynamic user equilibrium (DUE) models (Friesz et al. 1993).
Friesz TL, Han K, Meimand A, et al., 2012, Dynamic user equilibrium based on the hydrodynamic model, The 4th International Symposium on Dynamic Traffic Assignment
In this paper we present a continuous-time network loading procedure based on the Light- hill–Whitham–Richards model proposed by Lighthill and Whitham (1955) and Richards (1956). A system of differential algebraic equations (DAEs) is proposed for describing traffic flow propagation, travel delay and route choices. We employ a novel numerical apparatus to reformulate the scalar conservation law as a flow-based partial differential equation (PDE), which is then solved semi-analytically with the Lax–Hopf formula. This approach allows for an efficient computational scheme for large-scale networks. We embed this net- work loading procedure into the dynamic user equilibrium (DUE) model proposed by Friesz et al. (1993). The DUE model is solved as a differential variational inequality (DVI) using a fixed-point algorithm. Several numerical examples of DUE on networks of varying sizes are presented, including the Sioux Falls network with a significant number of paths and origin–destination pairs (OD).The DUE model presented in this article can be formulated as a variational inequality (VI) as reported in Friesz et al. (1993). We will present the Kuhn–Tucker (KT) conditions for that VI, which is a linear system for any given feasible solution, and use them to check whether a DUE solution has been attained. In order to solve for the KT multiplier we present a decomposition of the linear system that allows efficient computation of the dual variables. The numerical solutions of DUE obtained from fixed-point iterations will be tested against the KT conditions and validated as legitimate solutions.
Han K, Yao T, Friesz TL, Lagrangian-based hydrodynamic model: freeway traffic estimation, 4th International Symposium on Dynamic Traffic Assignment
Friesz TL, Han K, Meimand A, et al., Dynamic user equilibrium based on a hydrodynamic model, Transportation Research Board 91st Annual Meeting., Publisher: Transportation Research Board
Bressan A, Han K, 2011, Optima and Equilibria for a Model of Traffic Flow, SIAM Journal on Mathematical Analysis, Vol: 43, Pages: 2384-2417, ISSN: 0036-1410
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