32,380 research outputs found
A bi-level model of dynamic traffic signal control with continuum approximation
This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure
Steady-state traffic flow on a ring road with up- and down- slopes
This paper studies steady-state traffic flow on a ring road with up- and
down- slopes using a semi-discrete model. By exploiting the relations between
the semi-discrete and the continuum models, a steady-state solution is uniquely
determined for a given total number of vehicles on the ring road. The solution
is exact and always stable with respect to the first-order continuum model,
whereas it is a good approximation with respect to the semi-discrete model
provided that the involved equilibrium constant states are linearly stable. In
an otherwise case, the instability of one or more equilibria could trigger
stop-and-go waves propagating in certain road sections or throughout the ring
road. The indicated results are reasonable and thus physically significant for
a better understanding of real traffic flow on an inhomogeneous road
A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models
In the present paper a review and numerical comparison of a special class of
multi-phase traffic theories based on microscopic, kinetic and macroscopic
traffic models is given. Macroscopic traffic equations with multi-valued
fundamental diagrams are derived from different microscopic and kinetic models.
Numerical experiments show similarities and differences of the models, in
particular, for the appearance and structure of stop and go waves for highway
traffic in dense situations. For all models, but one, phase transitions can
appear near bottlenecks depending on the local density and velocity of the
flow
Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control
We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic
Long-lived states in synchronized traffic flow. Empirical prompt and dynamical trap model
The present paper proposes a novel interpretation of the widely scattered
states (called synchronized traffic) stimulated by Kerner's hypotheses about
the existence of a multitude of metastable states in the fundamental diagram.
Using single vehicle data collected at the German highway A1, temporal velocity
patterns have been analyzed to show a collection of certain fragments with
approximately constant velocities and sharp jumps between them. The particular
velocity values in these fragments vary in a wide range. In contrast, the flow
rate is more or less constant because its fluctuations are mainly due to the
discreteness of traffic flow.
Subsequently, we develop a model for synchronized traffic that can explain
these characteristics. Following previous work (I.A.Lubashevsky, R.Mahnke,
Phys. Rev. E v. 62, p. 6082, 2000) the vehicle flow is specified by car
density, mean velocity, and additional order parameters and that are
due to the many-particle effects of the vehicle interaction. The parameter
describes the multilane correlations in the vehicle motion. Together with the
car density it determines directly the mean velocity. The parameter , in
contrast, controls the evolution of only. The model assumes that
fluctuates randomly around the value corresponding to the car configuration
optimal for lane changing. When it deviates from this value the lane change is
depressed for all cars forming a local cluster. Since exactly the overtaking
manoeuvres of these cars cause the order parameter to vary, the evolution
of the car arrangement becomes frozen for a certain time. In other words, the
evolution equations form certain dynamical traps responsible for the long-time
correlations in the synchronized mode.Comment: 16 pages, 10 figures, RevTeX
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