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Boundary conditions and behavior of the macroscopic fundamental diagram based network traffic dynamics: A control systems perspective
(2018-05-01)
Zhong, R. X.
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Huang, Y. P.
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Chen, C.
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Lam, W. H.K.
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Xu, D. B.
Macroscopic fundamental diagram (MFD), establishing a mapping from the network flow accumulation to the trip completion rate, has been widely used for aggregate modeling of urban traffic network dynamics. Based on the MFD framework, extensive research has been dedicated to devising perimeter control strategies to protect the network from gridlock. Recent research has revealed that the stochasticity and time-varying nature of travel demand can introduce significant scattering in the MFD, thus reducing the definition of the MFD dynamics. However, this type of demand effect on the behavior of the MFD dynamics has not been well studied. In this article, we investigate such effect and propose some appropriate boundary conditions to ensure that the MFD dynamics are well-defined. These boundary conditions can be regarded as travel demand adjustment in traffic rationing. For perimeter control design, a set of sufficient conditions that guarantee the controllability, an important but yet untouched issue, are derived for general multi-region MFD systems. The stability of the network equilibrium and convergence of the network dynamics are then analyzed in the sense of Lyapunov. Both theoretical and numerical results indicate that the network traffic converges to the desired uncongested equilibrium under proper boundary conditions in conjunction with proper control measures. The results are consistent with some existing studies and offer a control systems perspective regarding the demand-oriented behavior analysis of MFD-based network traffic dynamics. A surprising finding is that if the control purpose is to regulate the traffic to a desired level of service, the perimeter control gain can be simply chosen as its desired steady state, that is, the control gain is a constant and can be implemented as proportional control. This property sheds light on the road pricing design based on the MFD framework by minimizing the gap between the actual traffic state and the desired traffic state.
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Forecasting journey time distribution with consideration to abnormal traffic conditions
(2017-12-01)
Zhong, R. X.
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Luo, J. C.
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Cai, H. X.
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Sumalee, A.
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Yuan, F. F.
Travel time is an important index for managers to evaluate the performance of transportation systems and an intuitive measure for travelers to choose routes and departure times. An important part of the literature focuses on predicting instantaneous travel time under recurrent traffic conditions to disseminate traffic information. However, accurate travel time prediction is important for assessing the effects of abnormal traffic conditions and helping travelers make reliable travel decisions under such conditions. This study proposes an online travel time prediction model with emphasis on capturing the effects of anomalies. The model divides a path into short links. A Functional Principal Component Analysis (FPCA) framework is adopted to forecast link travel times based on historical data and real-time measurements. Furthermore, a probabilistic nested delay operator is used to calculate path travel time distributions. To ensure that the algorithm is fast enough for online applications, parallel computation architecture is introduced to overcome the computational burden of the FPCA. Finally, a rolling horizon structure is applied to online travel time prediction. Empirical results for Guangzhou Airport Expressway indicate that the proposed method can capture an abrupt change in traffic state and provide a promising and reliable travel time prediction at both the link and path levels. In the case where the original FPCA is modified for parallelization, accuracy and computational effort are evaluated and compared with those of the sequential algorithm. The proposed algorithm is found to require only a piece rather than a large set of traffic incident records.
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A cross-entropy method and probabilistic sensitivity analysis framework for calibrating microscopic traffic models
(2016-02-01)
Zhong, R. X.
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Fu, K. Y.
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Sumalee, A.
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Ngoduy, D.
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Lam, W. H.K.
Car following modeling framework seeks for a more realistic representation of car following behavior in complex driving situations to improve traffic safety and to better understand several puzzling traffic flow phenomena, such as stop-and-go oscillations. Calibration and validation techniques pave the way towards the descriptive power of car-following models and their applicability for analyzing traffic flow. However, calibrating these models is never a trivial task. This is caused by the fact that some parameters, such as reaction time, are generally not directly observable from traffic data. On the other hand, traffic data might be subject to various errors and noises. This contribution puts forward a Cross-Entropy Method (CEM) based approach to identify parameters of deterministic car-following models under noisy data by formulating it as a stochastic optimization problem. This approach allows for statistical analysis of the parameter estimations. Another challenge arising in the calibration of car following models concerns the selection of the most important parameters. This paper introduces a relative entropy based Probabilistic Sensitivity Analysis (PSA) algorithm to identify the important parameters so as to reduce the complexity, data requirement and computational effort of the calibration process. Since the CEM and the PSA are based on the Kullback-Leibler (K-L) distance, they can be simultaneously integrated into a unified framework to further reduce the computational burden. The proposed framework is applied to calibrate the intelligent driving model using vehicle trajectories data from the NGSIM project. Results confirm the great potential of this approach.
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Optimal and robust strategies for freeway traffic management under demand and supply uncertainties: An overview and general theory
(2014-01-01)
Zhong, R. X.
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Sumalee, A.
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Pan, T. L.
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Lam, William H.K.
This paper investigates optimal decision-making for traffic management under demand and supply uncertainties by stochastic dynamic programming. Traffic flow dynamics under demand and supply uncertainties is described by a simplified version of the stochastic cell transmission model. Based on this model, the optimal traffic management problem is analysed wherein the existence of solution is guaranteed by verifying the well-posed condition. An analytical optimal control law is derived in terms of a set of coupled generalised recursive Riccati equations. As optimal control laws may be fragile with respect to model misspecification, a robust (optimal) decision-making law that aims to act robust with respect to the parameter misspecification in the traffic flow model (which can be originated from model calibration), and to attenuate the effect of disturbances in freeway networks (wherein demand uncertainty is usually regarded as a kind of disturbance) is proposed. Conventionally, network uncertainties have been considered to induce negative effects on traffic management in transportation literature. In contrast, the proposed methodology outlines an interesting issue that is to make benefit (or trade-off) from the inherent network uncertainties. Finally, some practical issues in traffic management that can be addressed by extending the current framework are briefly discussed. © 2014 Hong Kong Society for Transportation Studies Limited.

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