Lighthill-Whitham-Richards Model for Traffic Flow Mixed with Cooperative Adaptive Cruise Control Vehicles

Yanyan Qin (), Hao Wang () and Daiheng Ni ()
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Yanyan Qin: School of Traffic and Transportation, Chongqing Jiaotong University, Chongqing 400074, China; School of Transportation, Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 210096, China
Hao Wang: School of Transportation, Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 210096, China
Daiheng Ni: Department of Civil and Environmental Engineering, University of Massachusetts, Amherst, Massachusetts 01003

Transportation Science, 2021, vol. 55, issue 4, 883-907

Abstract: In the future, road traffic will incorporate a random mix of manual vehicles and cooperative adaptive cruise control (CACC) vehicles, where a CACC vehicle will degrade to an adaptive cruise control (ACC) vehicle when vehicle-to-vehicle communications are not available. This paper proposes a generalized framework of the Lighthill-Whitham-Richards (LWR) model for such mixed vehicular flow under different CACC penetration rates. In this approach, the kinematic wave speed propagating through the mixed platoon was theoretically proven to be the slope of mixed fundamental diagram. In addition, the random degradation from CACC to ACC was captured in mathematical expectation for traffic scenarios where the CACC only monitors one vehicle ahead. Three concrete car-following models, the intelligent driver model (IDM) and CACC/ACC models validated by Partners for Advanced Transit and Highways (PATH) program, were selected as examples to investigate the propagation of small perturbations and shock waves. Numerical simulations were also performed based on the selected car-following models. Moreover, the derived mixed LWR model was applied to solve some traffic flow problems. It indicates that the proposed LWR model is able to describe the propagation properties of both small perturbations and shock waves. The mixed LWR model can also be used to solve some practical problems, such as the queue caused by a traffic accident and the impact of a moving bottleneck. More importantly, the proposed generalized framework admits other CACC/ACC/regular car-following models, including those developed from further experiments.

Keywords: cooperative adaptive cruise control (CACC); mixed traffic flow; LWR model; simulations; car-following model; connected and automated vehicles (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:55:y:2021:i:4:p:883-907

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