Calibration of Dynamic Volume-Delay Functions: A Rolling Horizon-Based Parsimonious Modeling Perspective

Volume-delay functions (VDF) are the critical building block in static traffic assignment and general demand-supply analysis. This paper aims to provide a rolling horizon-based modeling framework to establish and further calibrate dynamic VDF (DVDF) for a corridor. The development and application of classic VDF in recent traffic planning studies are first reviewed. Analytical formulas based on a rolling horizon framework are then developed to redefine critical elements in the Bureau of Public Roads (BPR) function to capture the time-dependent volume-delay relationship. Time-dependent average demand and discharge rate are used in a real-world bottleneck in oversaturated conditions. By constructing an estimate or approximate for the dynamic degree of saturation, the proposed method could (i) better interpret the underlying mechanism of the time-dependent demand-delay function; (ii) provide a valuable tool to estimate the speed for a time rolling horizon with given real-time data in practice, and (iii) analyze the correlation between a bottleneck and upstream or downstream on a road network to acquire accurate discharge rates for different situations. Experiments using corridors in Beijing and Los Angeles demonstrate that the proposed dynamic analytical methods can outperform the traditional BPR function in dynamic congestion cases. The results improve the DVDF goodness-of-fit from R 2 of 44% to 87% under different conditions, which sheds more light on future online traffic simulation applications.

Automated summary

This study proposes a modeling framework based on a rolling window to establish and calibrate dynamic VDF, aiming to better interpret the time-dependent volume-delay relationship, provide a valuable tool for estimating the demand-delay function based on real-time data in practice, and analyze the correlation between bottlenecks and upstream or downstream on a road network to obtain accurate discharge rates in different situations.