37,565 research outputs found
Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA)
problem to design optimal traffic flow controls for freeway networks as modeled
by the Cell Transmission Model, using variable speed limit, ramp metering, and
routing. We consider two optimal control problems: the DTA problem, where
turning ratios are part of the control inputs, and the Freeway Network Control
(FNC), where turning ratios are instead assigned exogenous parameters. It is
known that relaxation of the supply and demand constraints in the cell-based
formulations of the DTA problem results in a linear program. However, solutions
to the relaxed problem can be infeasible with respect to traffic dynamics.
Previous work has shown that such solutions can be made feasible by proper
choice of ramp metering and variable speed limit control for specific traffic
networks. We extend this procedure to arbitrary networks and provide insight
into the structure and robustness of the proposed optimal controllers. For a
network consisting only of ordinary, merge, and diverge junctions, where the
cells have linear demand functions and affine supply functions with identical
slopes, and the cost is the total traffic volume, we show, using the maximum
principle, that variable speed limits are not needed in order to achieve
optimality in the FNC problem, and ramp metering is sufficient. We also prove
bounds on perturbation of the controlled system trajectory in terms of
perturbations in initial traffic volume and exogenous inflows. These bounds,
which leverage monotonicity properties of the controlled trajectory, are shown
to be in close agreement with numerical simulation results
Analysis of dynamic system optimal assignment with departure time choice
Most analyses on dynamic system optimal (DSO) assignment are done by using the
control theory with an outflow traffic model. On the one hand, this control theoretical
formulation provides some attractive mathematical properties for analysis. On the
other hand, however, this kind of formulation often ignores the importance of
ensuring proper flow propagation. Moreover, the outflow models have also been
extensively criticized for their implausible traffic behaviour. This paper aims to
provide another framework for analysing a DSO assignment problem based upon
sound traffic models. The assignment problem we considered aims to minimize the
total system cost in a network by seeking an optimal inflow profile within a fixed
planning horizon. This paper first summarizes the requirements on a plausible traffic
model and reviews three common traffic models. The necessary conditions for the
optimization problem are then derived using a calculus of variations technique.
Finally, a simple working example and some concluding remarks are given
Traffic models for dynamic system optimal assignment
Most analyses on dynamic system optimal (DSO) assignment are done by using a control theory
with an outflow traffic model. On the one hand, this control theoretical formulation provides some
attractive mathematical properties for analysis. On the other hand, however, this kind of formulation
often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models
have also been extensively criticized for their implausible traffic behaviour. This paper aims to
provide another framework for analysing a DSO assignment problem based upon sound traffic
models. The assignment problem we considered aims to minimize the total system cost in a
network by seeking an optimal inflow profile within a fixed planning horizon. This paper first
summarizes the requirements on a plausible traffic model and reviews three common traffic
models. The necessary conditions for the optimization problem are then derived using a calculus of
variations technique. Finally, a simple working example and concluding remarks are given
Toward a general framework for dynamic road pricing
This paper develops a general framework for analysing and calculating dynamic road toll. The
optimal network flow is first determined by solving an optimal control problem with statedependent
responses such that the overall benefit of the network system is maximized. An
optimal toll is then sought to decentralise this optimal flow. This control theoretic formulation
can work with general travel time models and cost functions. Deterministic queue is
predominantly used in dynamic network models. The analysis in this paper is more general
and is applied to calculate the optimal flow and toll for Friesz’s whole link traffic model.
Numerical examples are provided for illustration and discussion. Finally, some concluding
remarks are given
System optimizing flow and externalities in time-dependent road networks
This paper develops a framework for analysing and calculating system optimizing flow and
externalities in time-dependent road networks. The externalities are derived by using a novel
sensitivity analysis of traffic models. The optimal network flow is determined by solving a
state-dependent optimal control problem, which assigns traffic such that the total system cost
of the network system is minimized. This control theoretic formulation can work with general
travel time models and cost functions. Deterministic queue is predominantly used in dynamic
network models. The analysis in this paper is more general and is applied to calculate the
system optimizing flow for Friesz’s whole link traffic model. Numerical examples are
provided for illustration and discussion. Finally, some concluding remarks are given
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