Bayesian MCMC with Gibbs sampling for saturation flow rate estimation in heterogeneous traffic at pretimed signalized intersections

Pretimed signalized intersections significantly contribute to traffic congestion, especially under the heterogeneous traffic conditions commonly observed in emerging economies such as Indonesia. Accurate estimation of the base saturation flow rate (BSFR) is essential for reliable capacity assessment, which influences effective intersection design and operation. However, the current BSFR estimation methods outlined in the Indonesian Highway Capacity Guidelines (IHCG, 2023) rely on outdated linear models derived from the Indonesian Highway Capacity Manual (IHCM, 1997), which are inadequate for addressing contemporary heterogeneous traffic complexities. This study introduces a Bayesian Markov Chain Monte Carlo (MCMC) model employing Gibbs sampling to improve BSFR estimation accuracy. The Bayesian MCMC model achieved a Root Mean Square Error Approximation (RMSEA) of 8.638 % compared to the existing IHCG method, which produced an RMSEA of up to 51.428 %, enabling a more precise intersection capacity design. Additionally, the developed model reduced the BSFR overestimation associated with the IHCG method by approximately 42.79 %, highlighting the potential of Bayesian MCMC methods to effectively address heterogeneous traffic challenges, enhance traffic management strategies, and optimize intersection operations. The Bayesian approach provides a probabilistic framework for quantifying uncertainty, allows for the incorporation of prior knowledge to enhance parameter estimation flexibility, and effectively mitigates model overfitting. The developed model demonstrates robust statistical validity, characterized by a mean beta parameter value of 403.30, standard deviation of 8.66, and Monte Carlo Standard Error (MCSE) of 0.0008, confirming high reliability and predictive precision. The proposed BSFR model exhibited superior performance in fitting empirical data, as evidenced by an RMSE of 240.403 PCU/g/h/We and RMSEA of 8.638 %, indicating an excellent model fit within acceptable thresholds (<10 %).