Large-scale simulation of traffic flow using Markov model

Area of Science:

• Transportation Engineering
• Applied Mathematics
• Computer Science

Background:

• Traffic modeling is crucial for urban infrastructure management, traffic problem resolution, and real-time traffic adaptation.
• Existing stochastic models based on graph and Markov chain theories describe traffic dynamics using transition probability matrices and stationary distributions.
• These models, while rigorous, do not fully capture both traffic dynamics and vehicle distribution simultaneously.

Purpose of the Study:

• To present a novel parametrization for traffic modeling using a two-dimensional stationary distribution.
• To enhance existing stochastic models by integrating traffic dynamics with vehicle distribution.
• To apply and validate the proposed model and estimation method using real-world trajectory and road network data.

Main Methods:

• Introduced a new parametrization concept: two-dimensional stationary distribution.
• Applied the weighted least squares estimation method for parameter matrix estimation using trajectory data.
• Utilized the Taxi Trajectory Prediction dataset and OpenStreetMap road network data for case studies.

Main Results:

• The proposed model and weighted least squares estimation procedure demonstrated satisfactory performance on both artificial and real datasets.
• Simulations showed the new approach to be superior to the frequency-based maximum likelihood method.
• Successfully unfolded a stationary distribution on the map graph of Porto, showcasing practical applicability.

Conclusions:

• The novel two-dimensional stationary distribution model effectively handles both traffic dynamics and vehicle distribution in urban road networks.
• The weighted least squares estimation method provides a robust way to estimate model parameters from trajectory data.
• This combined approach offers a significant advancement in analyzing traffic on large-scale road networks, outperforming previous methods.