Conference Paper

Exact solutions to traffic density estimation problems involving the Lighthill-Whitham-Richards traffic flow model using Mixed Integer Programming

DOI: 10.1109/ITSC.2012.6338639 Conference: 15th International IEEE Conference on Intelligent Transportation Systems

ABSTRACT This article presents a new mixed integer programming formulation of the traffic density estimation problem in highways modeled by the Lighthill Whitham Richards equation. We first present an equivalent formulation of the problem using an Hamilton-Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton-Jacobi equation result in linear constraints, albeit with unknown integers. We then pose the problem of estimating the density at the initial time given
incomplete and inaccurate traffic data as a Mixed Integer Program. We then present a numerical implementation of the method using experimental flow and probe data obtained during Mobile Century experiment.

0 Bookmarks
 · 
81 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We propose a general traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as well as upstream demand of traffic wishing to flow through the junction. This approach is rooted in the celebrated Cell Transmission Model for freeway traffic flow. Unlike related results which rely on certain system cooperativity properties, our model generally does not possess these properties. We show that the lack of cooperativity is in fact a useful feature that allows traffic control methods, such as ramp metering, to be effective. Finally, we leverage the results of the paper to develop a linear program for optimal ramp metering.
    09/2014;
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a new wireless platform designed for an integrated traffic monitoring system based on combined Lagrangian (mobile) and Eulerian (fixed) sensing. The sensor platform is built around a 32-bit ARM Cortex M4 micro-controller and a 2.4GHz 802.15.4 ISM compliant radio module, and can be interfaced with fixed traffic sensors, or receive data from vehicle transponders. The platform is specially designed and optimized to be integrated in a solar-powered wireless sensor network in which traffic flow maps are computed by the nodes directly using distributed computing. A MPPT circuitry is proposed to increase the power output of the attached solar panel. A self-recovering unit is designed to increase reliability and allow periodic hard resets, an essential requirement for sensor networks. A radio monitoring circuitry is proposed to monitor incoming and outgoing transmissions, simplifying software debug. An ongoing implementation is briefly discussed, and compared with existing platforms used in wireless sensor networks.
    Industrial Embedded Systems (SIES), 2013 8th IEEE International Symposium on; 01/2013
  • [Show abstract] [Hide abstract]
    ABSTRACT: This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network.
    Control of Network Systems, IEEE Transactions on. 03/2014; 1(1):28-39.

Full-text

Download
44 Downloads
Available from
May 21, 2014