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Bayesian MCMC with Gibbs sampling for saturation flow rate estimation in heterogeneous traffic at pretimed signalized
Lulusi Lulusi1,2, Sugiarto Sugiarto2,3, Sofyan M Saleh2
1Doctoral Program, School of Engineering, Post Graduate Program, Universitas Syiah Kuala, Banda Aceh, 23111, Indonesia.
Methodsx
|July 31, 2025
Summary
A new Bayesian Markov Chain Monte Carlo (MCMC) model significantly improves base saturation flow rate (BSFR) estimation for pretimed signalized intersections. This advanced method enhances traffic capacity assessment and reduces overestimation compared to existing guidelines.
Area of Science:
- Traffic Engineering
- Transportation Science
- Statistical Modeling
Background:
- Pretimed signalized intersections are major contributors to traffic congestion, particularly in emerging economies with heterogeneous traffic.
- Accurate base saturation flow rate (BSFR) estimation is critical for effective intersection capacity assessment, design, and operation.
- Current Indonesian Highway Capacity Guidelines (IHCG, 2023) utilize outdated linear models (IHCM, 1997) inadequate for complex traffic conditions.
Purpose of the Study:
- To develop and validate an improved BSFR estimation model using Bayesian Markov Chain Monte Carlo (MCMC) methods.
- To enhance the accuracy of capacity assessment for signalized intersections under heterogeneous traffic.
- To address the limitations of existing BSFR estimation techniques in the Indonesian context.
Main Methods:
- Implementation of a Bayesian Markov Chain Monte Carlo (MCMC) model utilizing Gibbs sampling for BSFR estimation.
- Comparison of the proposed Bayesian MCMC model's performance against the existing IHCG method.
- Statistical validation using metrics such as Root Mean Square Error Approximation (RMSEA) and Root Mean Square Error (RMSE).
Main Results:
- The Bayesian MCMC model achieved a significantly lower RMSEA of 8.638% compared to the IHCG method's 51.428%.
- The developed model reduced BSFR overestimation by approximately 42.79% compared to the IHCG method.
- The model demonstrated robust statistical validity with a mean beta of 403.30 and low Monte Carlo Standard Error (MCSE) of 0.0008.
Conclusions:
- Bayesian MCMC methods offer a superior approach for BSFR estimation, effectively handling heterogeneous traffic complexities.
- The proposed model enhances intersection capacity design precision and optimizes traffic management strategies.
- The probabilistic framework of the Bayesian approach provides reliable uncertainty quantification and mitigates model overfitting.
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