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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.
;
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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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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Simultaneous optimization of fuel surcharges and transit service runs in a multimodal transport network: A time-dependent activity-based approach
(2016-01-01)
Li, Z. C.
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Yin, Y.
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Lam, W. H.K.
;
Sumalee, A.
This paper addresses the simultaneous optimization problem of fuel surcharges and transit service runs for energy sustainability of multimodal transport network using a time-dependent activity-based approach. To model commuters' choices of trip chain, travel mode, departure time, route, and activity timing and duration over the times of a day, a time-dependent activity and multimodal travel choice equilibrium problem is first addressed and formulated as an equivalent variational inequality (VI) problem. A new model for optimizing the fuel surcharges and transit vehicle runs is proposed to maximize the total social net benefit of the multimodal transport system. The proposed model explicitly considers the interaction between the fuel surcharges and transit service runs and the commuters' activity-travel scheduling behavior. A heuristic solution algorithm is then developed to solve the proposed model. Finally, an illustrative example is given to show the application of the proposed model with various sensitivity tests. Insightful findings are presented with particularly the effects of the fuel surcharges and transit service improvement on the performance of the multimodal transport system in terms of the modal split, fuel consumption, and total social net benefit.

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