First-order traffic flow models incorporating capacity drop: Overview and real-data validation

Kontorinaki, Maria; Spiliopoulou, Anastasia; Roncoli, Claudio; Papageorgiou, Markos

doi:10.1016/j.trb.2017.10.014

Cited by 73 publications

(51 citation statements)

References 51 publications

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“…This concept is similar to the empirical observation in [14]. Moreover, some contributions combine the bounded acceleration and lane changing effects for reproducing the capacity drop (e.g., Roncoli et al [22], Srivastava and Jin [23], Kontorinaki et al [24]). Those works let the demand decrease as the over-critical density increases.…”

Section: Introductionmentioning

confidence: 54%

“…Srivastava and Jin [23] use a concept of perceived density which is higher than the actually density, that origins from an assumption that the lane changing contribute to the density on both of original and target lanes. Kontorinaki et al [24] give more capacity to merge cells by modifying supply function to allow a density at the merge cells higher than the critical density. One drawback of those works considering merging, except [22], is that the outflow of stop-and-go waves on homogeneous road sections equals to the free-flow capacity.…”

Section: Introductionmentioning

confidence: 99%

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A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

Yuan

Knoop

Hoogendoorn

2017

Physica A: Statistical Mechanics and its Applications

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On freeways, congestion always leads to capacity drop. This means the queue discharge rate is lower than the pre-queue capacity. Our recent research findings indicate that the queue discharge rate increases with the speed in congestion, that is the capacity drop is strongly correlated with the congestion state. Incorporating this varying capacity drop into a kinematic wave model is essential for assessing consequences of control strategies. However, to the best of authors' knowledge, no such a model exists. This paper fills the research gap by presenting a Lagrangian kinematic wave model. "Lagrangian" denotes that the new model is solved in Lagrangian coordinates. The new model can give capacity drops accompanying both of stop-and-go waves (on homogeneous freeway section) and standing queues (at nodes) in a network. The new model can be applied in a network operation. In this Lagrangian kinematic wave model, the queue discharge rate (or the capacity drop) is a function of vehicular speed in traffic jams. Four case studies on links as well as at lane-drop and on-ramp nodes show that the Lagrangian kinematic wave model can give capacity drops well, consistent with empirical observations.

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Section: Introductionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

Yuan

Knoop

Hoogendoorn

2017

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Note that only the minimal demand function d e (·) has to satisfy Assumption 2. Hence, also demand functions with capacity drop (a decrease in demand above a critical density [18]) are contained in the uncertainty set Ω d .…”

Section: Model Descriptionmentioning

confidence: 99%

An exact convex relaxation of the freeway network control problem with controlled merging junctions

Schmitt

Lygeros

2018

Transportation Research Part B: Methodological

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In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging flows are controlled, there exist tight convex relaxations of the corresponding optimization problem. However, model uncertainty, in particular regarding the fundamental diagram and predictions of future traffic demand, can be a problem in practice. This uncertainty poses a challenge to control approaches that pursue a model-and optimization-based strategy. In this work, we propose a robust counterpart to the FNC problem, where we introduce uncertainty sets for both the fundamental diagram and future, external traffic demands and seek to optimize the system operation, minimizing the worst-case cost. For a network with controlled merging junctions, and assuming that certain technical conditions on the uncertainty sets are satisfied, we show that the robust counterpart of the FNC problem can be reduced to a convex, finite-dimensional and deterministic optimization problem, whose numerical solution is tractable.

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“…Finally, recall that the theoretical analysis in this work applies to the monotonic CTM. We will also extend the empirical analysis to a non-monotonic variation 5 of the fundamental diagram as depicted in Figure 10c [15].…”

Section: Model Uncertaintymentioning

confidence: 99%

Sufficient optimality conditions for distributed, non-predictive ramp metering in the monotonic cell transmission model

Schmitt¹,

Ramesh²,

Lygeros³

2017

Transportation Research Part B: Methodological

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We consider the ramp metering problem for a freeway stretch modeled by the Cell Transmission Model. Assuming perfect model knowledge and perfect traffic demand prediction, the ramp metering problem can be cast as a finite horizon optimal control problem with the objective of minimizing the Total Time Spent, i.e., the sum of the travel times of all drivers. For this reason, the application of Model Predictive Control (MPC) to the ramp metering problem has been proposed. However, practical tests on freeways show that MPC may not outperform simple, distributed feedback policies. Until now, a theoretical justification for this empirical observation was lacking. This work compares the performance of distributed, non-predictive policies to the optimal solution in an idealised setting, specifically, for monotonic traffic dynamics and assuming perfect model knowledge. To do so, we suggest a distributed, non-predictive policy and derive sufficient optimality conditions for the minimization of the Total Time Spent via monotonicity arguments. In a case study based on real-world traffic data, we demonstrate that these optimality conditions are only rarely violated. Moreover, we observe that the suboptimality resulting from such infrequent violations appears to be negligible. We complement this analysis with simulations in non-ideal settings, in particular allowing for model mismatch, and argue that Alinea, a successful, distributed ramp metering policy, comes close to the ideal controller both in terms of control behavior and in performance.

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First-order traffic flow models incorporating capacity drop: Overview and real-data validation

Cited by 73 publications

References 51 publications

A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

An exact convex relaxation of the freeway network control problem with controlled merging junctions

Sufficient optimality conditions for distributed, non-predictive ramp metering in the monotonic cell transmission model

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