80 research outputs found
Continuity of the Effective Path Delay Operator for Networks Based on the Link Delay Model
This paper is concerned with a dynamic traffic network performance model,
known as dynamic network loading (DNL), that is frequently employed in the
modeling and computation of analytical dynamic user equilibrium (DUE). As a key
component of continuous-time DUE models, DNL 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, by introducing
appropriate dynamics to flow propagation, flow conservation, and travel delays.
The DNL procedure gives rise to the path delay operator, which associates a
vector of path flows (path departure rates) with the corresponding path travel
costs. In this paper, we establish strong continuity of the path delay operator
for networks whose arc flows are described by the link delay model (Friesz et
al., 1993). Unlike result established in Zhu and Marcotte (2000), our
continuity proof is constructed without assuming a priori uniform boundedness
of the path flows. Such a more general continuity result has a few important
implications to the existence of simultaneous route-and-departure choice DUE
without a priori boundedness of path flows, and to any numerical algorithm that
allows convergence to be rigorously analyzed.Comment: 12 pages, 1 figur
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
Existence of simultaneous route and departure choice dynamic user equilibrium
This paper is concerned with the existence of the simultaneous
route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous
time, first formulated as an infinite-dimensional variational inequality in
Friesz et al. (1993). In deriving our existence result, we employ the
generalized Vickrey model (GVM) introduced in and to formulate the underlying
network loading problem. As we explain, the GVM corresponds to a path delay
operator that is provably strongly continuous on the Hilbert space of interest.
Finally, we provide the desired SRDC-DUE existence result for general
constraints relating path flows to a table of fixed trip volumes without
invocation of a priori bounds on the path flows.Comment: 21 page
Dynamic Congestion and Tolls with Mobile Source Emission
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 program with
equilibrium constraints (MPEC) problem and then reformulated as a mathematical
program 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.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the
Proceedings of the 20th International Symposium on Transportation and Traffic
Theory, 2013, the Netherland
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