A traffic-fractal-element-based congestion model considering the uneven distribution of road traffic

Abstract

The uneven distribution of road traffic has been proven to play a crucial role in congestion evolution within urban transportation networks. Establishing congestion models to explore congestion evolution under its impact is of great significance for predicting congestion. Current congestion models commonly describe the uneven distribution of traffic on roads through continuous differential equations or the simulation of vehicle operational rules by which to model traffic flow dynamics. However, these models fail to directly reveal the mechanism by which the uneven distribution characteristics affect congestion, which is not conducive to uncovering the fundamental factors that affect congestion evolution and general laws for predicting congestion. Therefore, this paper first constructs traffic fractal elements (TFE) based on the fractal characteristics exhibited by uneven traffic distribution. A local parameter namely the load duty ratio (LDR) is introduced to represent the uneven distribution level of TFE. By employing the fractal interpolation function (FIF), we model road traffic as the iterations of TFE. Then we define the fractal evolution rule and the load transfer rule to inscribe the influence relationship between LDR of TFE and global congestion, ultimately establishing a TFE-based congestion model. Furthermore, the proposed TFE-based model is validated using empirical data from AMAP and simulation data from a calibrated Cellular Automata (CA) model. Finally, by comparing the results with a CA-based congestion model, the LDR of TFE is confirmed to be a comprehensive and indicative parameter affecting congestion evolution. By simulating and fitting the congestion evolution data under different LDRs, our proposed model demonstrates its value in congestion prediction and analysis.