Automatic Identification of Near-Stationary Traffic States and Application on Multi-Lane Multi-Class Fundamental Diagram Calibration
Experience of daily commuters shows that stationary traffic patterns can be observed during peak periods in urban freeway networks. Such stationary states play an important role in many traffic flow studies. Theoretically, studies on the impact of capacity drop and design of traffic control strategies have been built on the assumption of stationarity. Mathematically, the existence and stability of stationary road networks have been proved within the framework of kinematic wave theories. Empirically, near-stationary states have been utilized for calibration of fundamental diagrams and investigation of traffic features at freeway bottlenecks. Therefore, an imperative need for real-world near-stationary data has been recognized to better understand and explore such above studies. However, there lacks an efficient method to identify near-stationary states.
In this research, an automatic method has been developed to efficiently identify near-stationary states from large amounts of inductive loop-detector data to fill the gap. The method consists of four steps: first, a data pre-processing technique is performed to select healthy datasets with sufficient congestion periods and normalize vehicle counts and occupancies to the same scale; second, a PELT changepoint detection method is applied to partitioning time series into candidate intervals; third, informative characteristics of each candidate, including duration and gap, are calculated; finally, near-stationary states are selected from candidates based on two well-designed selection criteria.
To calibrate two critical parameters of the method, a multi-objective optimization problem is formulated to consider the quantity and quality of near-stationary states as objective functions. Then a game theory approach is designed to convert the problem into a non-cooperative game. Further a game theory search algorithm with a built-in modified hill-climbing technique is developed to solve the game and obtain a unique Nash equilibrium solution. In an extended paradigm, a five-player game is built to achieve better performance on the near-stationary flow-occupancy pattern in the congested regime.
In an application, a calibration method of multi-lane multi-class fundamental diagrams with unifiable and non-FIFO properties is performed using identified near-stationary states. Results show that the calibrated multi-lane multi-class fundamental diagrams are well-fitted, physically meaningful, and have robust performance on the estimation and prediction of commodity flow-rates.