Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

Sutarto, Herman Y.; Boel, René; Joelianto, Endra · 2015 · OpenAlex-citations

DOI: 10.1049/iet-cta.2014.0909

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Summary

This paper addresses the challenge of estimating parameters for a stochastic hybrid model used to describe urban traffic flow in networks with signalized intersections. The motivation stems from the need for accurate dynamic models to support model-based control strategies, such as optimizing traffic light switching times to reduce congestion, emissions, and fuel consumption. Existing single-model approaches fail to capture the mode-dependent variance of traffic data, leading to poor estimation performance. To address this, the authors propose a stochastic hybrid model that accounts for different traffic operation modes—free-flowing, congested, and faulty—where the traffic flow rate evolves as a mode-dependent first-order autoregressive (AR) process. Mode switching is governed by a first-order Markov chain, creating a jump Markov process. The methodology involves an Expectation-Maximization (EM) technique to estimate the 15 parameters of the model: three AR parameters (intercept, coefficient, and noise variance) for each of the three modes, and the transition probabilities of the Markov chain. The EM algorithm operates in an offline batch mode, using a given sequence of traffic flow measurements. The E-step calculates smoothed inferences (conditional probabilities of the active mode given all observations) using forward filtering and backward smoothing recursions. The M-step updates the parameter estimates by maximizing a weighted log-likelihood function, where weights are derived from the smoothed inferences. The study utilizes real-world traffic data collected from video-type sensors at two neighboring intersections (313 and 314) in Jakarta, Indonesia. The sensors detect vehicle counts per traffic light cycle, which are converted into flow rates. The model assumes a fluid-flow approximation, treating vehicle counts as continuous variables averaged over cycle periods. The paper details the mathematical formulation of the EM algorithm, including the derivation of explicit formulas for updating AR parameters and transition probabilities. The proposed approach is validated using the actual Jakarta traffic data. The authors demonstrate that the EM technique successfully identifies the parameters of the hybrid model. Furthermore, they introduce a time window shift technique that allows for periodic updates of the model parameters, facilitating an adaptive traffic flow state estimator. The validated model is shown to be capable of estimating and predicting traffic flow rates and queue lengths at signalized intersections. The significance of this work lies in providing a robust, data-driven method for parameter estimation in stochastic hybrid traffic models. By accurately capturing the variability and mode-dependent characteristics of urban traffic, the model enables more precise probabilistic predictions of future traffic flows and queue lengths. This capability is a prerequisite for implementing effective real-time, model-predictive feedback controllers for traffic lights. The adaptive nature of the proposed estimator, combined with its ability to handle noisy sensor data and detect faults, makes it a practical tool for improving traffic management in complex urban environments.

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• mental model of traffic