A multi-layer multiclass cell transmission model for modeling heterogeneous traffic flow

Abstract

Modeling heterogeneous traffic with different free-flow speeds poses theoretical challenges for the existing multiclass cell transmission models (MCTMs) with identical cells. Specifically, the existing MCTMs face two challenges due to the numerical diffusion: delaying flow and rushing flow. These challenges arise because slow vehicles cannot travel through a cell within a time interval under free-flow conditions, leading to inaccurate estimates of cell occupancy and travel time. To address these challenges, we propose a Multi-layer Multiclass Cell Transmission Model (MMCTM) with multi-size cells. Firstly, a road is divided into a multi-layer multi-size cell network based on different free-flow speeds of multiclass vehicles. Class-specific vehicles move within a class-specific cell network, while other class vehicles are equivalently projected into class-specific cells using density mutual projection formulas. Secondly, we formulate the flow propagation rules for multiclass vehicles based on the original rules of CTM and conversion coefficients of different classes. We prove the capability of the MMCTM by showing that it can avoid unrealistic situations where the densities in the cells are negative or exceed the maximum density. Finally, numerical experiments demonstrate that our proposed model can effectively address the two challenges and reproduce essential phenomena of mixed traffic flow, such as the moving bottleneck effect of slow vehicles, shockwave propagation, overtaking, FIFO, and oscillatory waves. In particular, the MMCTM can reproduce the drop and resurge of the discharge rate of fast vehicles. Furthermore, we calibrate and validate the MMCTM using NGSIM I-80 dataset and the I-24 MOTION dataset. The results indicate that (1) our proposed model improves the estimation accuracy of travel time and cell occupancy for multiclass vehicles; (2) the MMCTM outperforms the general MCTM with identical cells (GMCTM) under traffic congestion conditions.