6,078 research outputs found
A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control
This paper is concerned with adaptive signal control problems on a road
network, using a link-based kinematic wave model (Han et al., 2012). Such a
model employs the Lighthill-Whitham-Richards model with a triangular
fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is
applied so that the system dynamics can be determined without knowledge of the
traffic state in the interior of each link. A Riemann problem for the
signalized junction is explicitly solved; and an optimization problem is
formulated in continuous-time with the aid of binary variables. A
time-discretization turns the optimization problem into a mixed integer linear
program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang,
2004; Lo, 1999b), the proposed framework does not require modeling or
computation within a link, thus reducing the number of (binary) variables and
computational effort.
The proposed model is free of vehicle-holding problems, and captures
important 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.Comment: 15 pages, 7 figures, current version is accepted for presentation at
the 92nd Annual Meeting of Transportation Research Boar
Lagrangian-based Hydrodynamic Model: Freeway Traffic Estimation
This paper is concerned with highway traffic estimation using traffic sensing
data, in a Lagrangian-based modeling framework. We consider the
Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards,
1956) in Lagrangian-coordinates, and provide rigorous mathematical results
regarding the equivalence of viscosity solutions to the Hamilton-Jacobi
equations in Eulerian and Lagrangian coordinates. We derive closed-form
solutions to the Lagrangian-based Hamilton-Jacobi equation using the Lax-Hopf
formula (Daganzo, 2005; Aubin et al., 2008), and discuss issues of fusing
traffic data of various types into the Lagrangian-based H-J equation. A
numerical study of the Mobile Century field experiment (Herrera et al., 2009)
demonstrates the unique modeling features and insights provided by the
Lagrangian-based approach.Comment: 17 pages, 7 figures, current version submitted to Transportation
Research Part
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