Flow-maximizing equilibria of the Cell Transmission Model

Schmitt, Marius; Goulart, Paul J.; Georghiou, Angelos; Lygeros, John

doi:10.1109/ecc.2015.7330935

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…At each iteration k, the upper-bounding problem (UBP k ) has the following form: (16), integer cuts (17).…”

Section: Solution Techniques For Nonconvex Problem (P3)mentioning

confidence: 99%

“…At each iteration k, the upper-bounding problem (UBP k ) has the following form: no congestion {(8), (12), ( 13), ( 14), (15)}, McCormick envelope (16), integer cuts (17).…”

Section: Solution Techniques For Nonconvex Problem (P3)mentioning

confidence: 99%

“…More recently, variable speed limits have been proposed as an effective congestion control mechanism in transportation [11]- [14]. Such works exploit the Cell Transmission Model to capture the deterministic distribution of traffic densities along a road [15], [16]. In practice, these approaches may be limited, due to the uncertainty on traffic density subject to unknown actions by various drivers as well as vehicle arrival and departure.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Data-Driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

Fooladivanda

Martínez

2019

2019 18th European Control Conference (ECC)

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This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.

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“…At each iteration k, the upper-bounding problem (UBP k ) has the following form: (16), integer cuts (17).…”

Section: Solution Techniques For Nonconvex Problem (P3)mentioning

confidence: 99%

“…At each iteration k, the upper-bounding problem (UBP k ) has the following form: no congestion {(8), (12), ( 13), ( 14), (15)}, McCormick envelope (16), integer cuts (17).…”

Section: Solution Techniques For Nonconvex Problem (P3)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Data-Driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

Fooladivanda

Martínez

2019

2019 18th European Control Conference (ECC)

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“…Instead of using model knowledge to estimate and predict split ratios and traffic demand and supply, this controller relies on integral feedback. Closed loop equilibria of Alinea in the monotonic CTM are known to be flow optimal [26].…”

Section: Nominal Casementioning

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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“…Ramp metering refers to the active control of the inflow of cars on a freeway via the onramps, by means of traffic lights [16], [17]. We consider a (quasi-) steadystate situation as in [18], in which the traffic demand cannot be completely served, a common occurrence during rushhour periods. Using our theoretical results, we can prove that for the commonly used monotone Cell Transmission Model (CTM) [19], [20], there does not exist a control policy that improves average demand satisfaction over the one achieved in the optimal equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Convex, monotone systems are optimally operated at steady-state

Schmitt

Ramesh

Goulart

et al. 2017

2017 American Control Conference (ACC)

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We consider a special class of monotone systems for which the system equations are also convex in both the state and the input. For such systems we study optimal infinite horizon operation with respect to an objective function that is also monotone and convex. The main results state that, under some technical assumptions, these systems are optimally operated at steady state, i.e. there does not exist any timevarying trajectory over an infinite horizon that outperforms stabilizing the system in the optimal equilibrium. We draw a connection to recent results on dissipative systems in the context of Economic Model Predictive Control, where systems that are optimally operated at steady state have already been studied. Finally, we apply the main result to a problem in traffic control, where we are able to disprove the existence of improving periodic trajectories involving the alternation of congestion and free flow for freeway ramp metering.

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Flow-maximizing equilibria of the Cell Transmission Model

Cited by 4 publications

References 18 publications

Data-Driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

Data-Driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

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

Convex, monotone systems are optimally operated at steady-state

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