First order velocity based travel time model (original) (raw)

Second-order fluid dynamics models for travel times in dynamic transportation networks

Concerns traffic congestion, especially in intelligent vehicle highway systems (IVHS); addressing such questions as how traffic patterns form and how congestion can be alleviated. Understanding drivers' travel times is key to this problem. We present macroscopic models for determining analytical forms for travel times. We take a fluid dynamics approach. We propose two second-order nonseparable macroscopic models for analytically estimating travel time functions : the polynomial travel time (PTT) model and the exponential travel time (ETT) model. These models incorporate second-order effects such as reaction of drivers to upstream and downstream congestion. Based on piecewise linear and piecewise quadratic approximations of the departure flow rates, we propose different classes of travel time functions for the first-order separable PTT and ETT models, and present the relationship between these functions. We show how the analysis of the first-order separable PTT model extends to t...

Real-Time Solution of Velocity-Based First-Order Continuum Traffic Model with Finite Element Method

Transportation Research Record: Journal of the Transportation Research Board, 2011

Two approximate solution methods are investigated for the velocity-based version of a first-order continuum traffic flow model commonly known as the Lighthill–Whitham–Richards model. The finite difference and finite element methods are commonly used to numerically solve partial differential equations. The finite difference method adopted uses a standard Godunov scheme to solve the continuum model. The finite element method uses one-dimensional simplex elements with first-order interpolation function along with a Galerkin scheme to derive the element characteristic matrices and vectors. A high-resolution, real-world data set from the Next Generation Simulation program is used to evaluate the two solution methods. Results show that both methods provide accurate approximations to the observed speeds. The accuracy and quality of solutions and future directions of work in this area are discussed.

A finite difference scheme for a macroscopic traffic flow model based on a nonlinear density-velocity relationship

Bangladesh Journal of Scientific and Industrial Research, 2012

We consider a macroscopic traffic flow model tagged on a closure nonlinear density-velocity relationship yielding a quasi-linear first order (hyperbolic) partial differential equation (PDE) as an initial boundary value problem (IBVP). We present the analytic solution of the PDE which is in implicit form. We describe the derivation of a finite difference scheme of the IBVP which is a first order explicit upwind difference scheme. We establish the well-posed-ness and stability condition of the finite difference scheme. To implement the numerical scheme we develop computer program using MATLAB programming language in order to verify some qualitative behaviors for various traffic parameters. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13070 Bangladesh J. Sci. Ind. Res. 47(3), 339-346 2012

TRAVEL TIME ESTIMATION: NEW THEORY DEVELOPMENT AND LARGE SCALE EVALUATION

ABSTRACT In this paper a new method is presented for estimating off-line travel times out of speed measurements along a route. The speed is being sampled at separated points and traffic flow is considered uninterrupted, like on a motorway for example. Different existing methods are compared to a new method and a validation is made on a 40km long highway road.* Keywords: Travel time estimation; Traffic flow theory; Dual loop detectors; Vehicle trajectories

Freeway travel-time estimation based on temporal–spatial queueing model

Travel time serves as a fundamental measurement for transportation systems and becomes increasingly important to both drivers and traffic operators. Existing speed interpolation algorithms use the average speed time series collected from upstream and downstream detectors to estimate the travel time of a road link. Such approaches often result in inaccurate estimations or even systematic bias, particularly when the real travel times quickly vary. To get rid of this problem, Coifman proposed a creative interpolation algorithm based on kinetic-wave models. This algorithm reconstructs vehicle trajectories according to the velocities and the headways of vehicles. However, it sometimes gives significant biased estimation, particularly when jams emerge from somewhere between the upstream and downstream detectors. To make an amendment, we design a new algorithm based on the temporal-spatial queueing model to describe the fast travel-time variations using only the speed and headway time series that is measured at upstream and downstream detectors. Numerical studies show that this new interpolation algorithm could better utilize the dynamic traffic flow information that is embedded in the speed/headway time series in some special cases.

Real-time travel time estimation using macroscopic traffic flow models

International Conference on Intelligent Transportation, 2001

This paper presents the estimation of travel time on highways based on macroscopic modelling. The focus is on real-time values as compared to average or static values. The macroscopic models are used for distributed and time/space lumped settings and corresponding travel time estimation functions and algorithms are developed. The implications of these algorithms for the implementation of various incident management