Robust controls for traffic networks: The near-Bayes near-Minimax strategy

Jones, L.; Deshpande, Rahul; Gartner, Nathan H.; Stamatiadis, C.; Zou, Fei

doi:10.1016/j.trc.2012.06.009

Cited by 10 publications

(2 citation statements)

References 19 publications

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“…In response to changing traffic flow patterns, some researchers studied the benefits of adjusting offsets or green times in real time for coordinated systems with actuated controllers [34]- [38]. Jones et al [39] propose a robust control approach that combines Bayes and Minimax to handle the uncertainty in origin-destination demands.…”

Section: Introductionmentioning

confidence: 99%

Bandwidth Synchronization Under Progression Time Uncertainty

2014

IEEE Trans. Intell. Transport. Syst.

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Deterministic progression time is generally assumed in bandwidth optimization models. However, progression time is cycle-by-cycle time varying and generally longer than the deterministic value. Progression time uncertainty has a considerable impact on the bandwidth that is obtained with deterministic data. In addition, we prove that there exist infinite optimal solutions in the MAXBAND model if a known optimal solution holds some properties. Different optimal solutions may have different sensitivities to progression time uncertainty. In this paper, we develop a two-phase approach. In the first phase we solve the MAXBAND models with perturbation controlled by a parameter and generate a number of optimal or suboptimal plans, and in the second phase we apply the Monte Carlo method to simulate random progression time, evaluate the generated plans, and rank them by the reliability. We also conduct extensive microscopic traffic simulation using VISSIM to evaluate delays and stops for certain optimal plans. Some observations are made.Index Terms-Bandwidth model, Monte Carlo method, multiple optimal solutions, progression time variation.

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Section: Introductionmentioning

confidence: 99%

Bandwidth Synchronization Under Progression Time Uncertainty

2014

IEEE Trans. Intell. Transport. Syst.

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“…Ukkusuri et al[13] proposed a robust optimal traffic signal control approach for urban networks with the future demand assumed to be uncertain, and they developed a robust system-optimal control approach with an embedded cell transmission model. Similarly considering the uncertainties in the origin-destination demands, Jones et al [14] proposed the near-Bayes near-Minimax method for robust traffic signal control for an urban network and obtained a good compromise solution between the Bayes case and the Minimax case. Tettamanti et al [15] developed a min-max MPC approach for urban networks to minimize the objective function in the worst-case scenario.…”

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confidence: 99%

Robust receding horizon parameterized control for multi‐class freeway networks: A tractable scenario‐based approach

Liu

Sadowska

Frejo

et al. 2016

Intl J Robust & Nonlinear

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In this paper, we propose a tractable scenario-based receding horizon parameterized control (RHPC) approach for freeway networks. In this approach, a scenario-based min-max scheme is used to handle uncertainties. This scheme optimizes the worst case among a limited number of scenarios that are considered. The use of parameterized control laws allows us to reduce the computational burden of the robust control problem based on the multi-class METANET model w.r.t. conventional model predictive control. To assess the performance of the proposed approach, a simulation experiment is implemented, in which scenario-based RHPC is compared with nominal RHPC, standard control ignoring uncertainties, and standard control including uncertainties. Here, the standard control approaches refer to state feedback controllers (such as PI-ALINEA for ramp metering). A queue override scheme is included for extra comparison. The results show that nominal RHPC approaches and standard control ignoring uncertainties may lead to high queue length constraint violations, and including a queue override scheme in standard control may not reduce queue length constraint violations to a low level. Including uncertainties in standard control approaches can obviously reduce queue length constraint violations, but the performance improvements are minor. For the given case study, scenario-based RHPC performs best as it is capable of improving control performance without high queue length constraint violations.In contrast, in heterogeneous multi-class models, these differences are considered, and vehicles are divided into different classes, such as cars, trucks, vans, and so on. The density of vehicles can be maintained around a critical value corresponding to maximum flow with a single-class fundamental diagram for mixed traffic. However, for model predictive control (MPC), in which the objective function depends on the dynamics of the controlled system, a more accurate model implies better prediction of future characteristics of the controlled system; thus, the controller has better information for determining control inputs. In general, the heterogeneous multi-class models are more accurate than homogeneous sing-class models, without increasing the computing complexity significantly. Some researchers have investigated the advantages of multi-class models. Wong and Wong [5] extended the Lighthill-Whitham-Richards (LWR) model to a multi-class version and found that the multi-class LWR model can reproduce some traffic phenomena (e.g., two-capacity phenomenon, hysteresis phenomenon of phase transition and platoon dispersion) that the single-class case cannot reproduce. Schreiter et al.[6] developed a multi-class controller that rerouted the traffic class specifically and showed that a multi-class controller outperformed a single-class controller. Liu et al. [7] extended METANET to a multi-class version, in which each vehicle class is assumed to be limited within its assigned space of the road, subjecting to its own fundamental diagram. Note, however, t...

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Uniformly Generating Origin Destination Tables

Einstein

Jones

2013

Information Theory, Combinatorics, and Search Theory

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Robust controls for traffic networks: The near-Bayes near-Minimax strategy

Cited by 10 publications

References 19 publications

Bandwidth Synchronization Under Progression Time Uncertainty

Bandwidth Synchronization Under Progression Time Uncertainty

Robust receding horizon parameterized control for multi‐class freeway networks: A tractable scenario‐based approach

Uniformly Generating Origin Destination Tables

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