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Flexible calibration of Dynamic Traffic Assignment (DTA) systems in real-time has important applications in effective traffic management. However, the existing approaches are either limited to small networks or to a specific class of parameters. In this light, this study presents a framework to systematically reduce the dimension of the generic online calibration problem making it more scalable. Specifically, we propose a state-space formulation of the problem in the reduced dimension space. Following which the problem is solved using the Constrained Extended Kalman Filter, which is made tractable because of the low dimensionality of the formulated problem. The effectiveness of the proposed approach is demonstrated using a real-world network leading to better state estimation by 13% and better state predictions by 11%-with a 50 fold dimensionality reduction. Insights into choosing the right degree of dimensionality reduction are also discussed. This work has the potential for a more widespread application of real-time DTA systems in practice.

The calibration of dynamic traffic assignment (DTA) models involves the estimation of model parameters to best replicate real-world measurements. Good calibration is essential to estimate and predict accurately traffic states, which are crucial for traffic management applications to alleviate congestion. A widely used approach to calibrate simulation-based DTA models is the extended Kalman filter (EKF). The EKF assumes that the DTA model parameters are unconstrained, although they are in fact constrained; for instance, origin–destination (O-D) flows are nonnegative. This assumption is typically not problematic for small- and medium-scale networks in which the EKF has been successfully applied. However, in large-scale networks (which typically contain numbers of O-D pairs with small magnitudes of flow), the estimates may severely violate constraints. In consequence, simply truncating the infeasible estimates may result in the divergence of EKF, leading to extremely poor state estimations and predictions. To address this issue, a constrained EKF (CEKF) approach is presented; it imposes constraints on the posterior distribution of the state estimators to obtain the maximum a posteriori (MAP) estimates that are feasible. The MAP estimates are obtained with a heuristic followed by the coordinate descent method. The procedure determines the optimum and are computationally faster by 31.5% over coordinate descent and by 94.9% over the interior point method. Experiments on the Singapore expressway network indicated that the CEKF significantly improved model accuracy and outperformed the traditional EKF (up to 78.17%) and generalized least squares (up to 17.13%) approaches in state estimation and prediction.

Effective real-time traffic management strategies often require Dynamic Traffic Assignment systems that are calibrated online. But the computationally intensive nature of online calibration limits their application to smaller networks. This paper presents a principal component based dimensionality reduction of the online calibration problem, which overcomes this limitation. To demonstrate this approach, we formulate the origin-destination flow estimation problem in terms of their principal components. The efficacy of the procedure is tested using real data on Singapore Expressway network in an open loop framework. We observe a reduction in the problem dimension by a factor of 50 with only 2% loss in estimation accuracy. Further, the computational times reduced by an order of 100. Interestingly, the procedure led to better predictions as the principal components capture the structural spatial relationships. This work has the potential to make the online calibration problem more scalable.

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