266 research outputs found
A kinematic wave theory of capacity drop
Capacity drop at active bottlenecks is one of the most puzzling traffic
phenomena, but a thorough understanding is practically important for designing
variable speed limit and ramp metering strategies. In this study, we attempt to
develop a simple model of capacity drop within the framework of kinematic wave
theory based on the observation that capacity drop occurs when an upstream
queue forms at an active bottleneck. In addition, we assume that the
fundamental diagrams are continuous in steady states. This assumption is
consistent with observations and can avoid unrealistic infinite characteristic
wave speeds in discontinuous fundamental diagrams. A core component of the new
model is an entropy condition defined by a discontinuous boundary flux
function. For a lane-drop area, we demonstrate that the model is well-defined,
and its Riemann problem can be uniquely solved. We theoretically discuss
traffic stability with this model subject to perturbations in density, upstream
demand, and downstream supply. We clarify that discontinuous flow-density
relations, or so-called "discontinuous" fundamental diagrams, are caused by
incomplete observations of traffic states. Theoretical results are consistent
with observations in the literature and are verified by numerical simulations
and empirical observations. We finally discuss potential applications and
future studies.Comment: 29 pages, 10 figure
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
On the optimization of conservation law models at a junction with inflow and flow distribution controls
The paper proposes a general framework to analyze control problems for
conservation law models on a network. Namely we consider a general class of
junction distribution controls and inflow controls and we establish the
compactness in of a class of flux-traces of solutions. We then derive the
existence of solutions for two optimization problems: (I) the maximization of
an integral functional depending on the flux-traces of solutions evaluated at
points of the incoming and outgoing edges; (II) the minimization of the total
variation of the optimal solutions of problem (I). Finally we provide an
equivalent variational formulation of the min-max problem (II) and we discuss
some numerical simulations for a junction with two incoming and two outgoing
edges.Comment: 29 pages, 14 figure
Riemann problems with non--local point constraints and capacity drop
In the present note we discuss in details the Riemann problem for a
one--dimensional hyperbolic conservation law subject to a point constraint. We
investigate how the regularity of the constraint operator impacts the
well--posedness of the problem, namely in the case, relevant for numerical
applications, of a discretized exit capacity. We devote particular attention to
the case in which the constraint is given by a non--local operator depending on
the solution itself. We provide several explicit examples. We also give the
detailed proof of some results announced in the paper [Andreainov, Donadello,
Rosini, "Crowd dynamics and conservation laws with non--local point constraints
and capacity drop", which is devoted to existence and stability for a more
general class of Cauchy problems subject to Lipschitz continuous non--local
point constraints.Comment: 19 pages, 6 figures. arXiv admin note: substantial text overlap with
arXiv:1304.628
- …