Delayed Lagrangian continuum models for on-board traffic prediction

Abstract In this paper we build Lagrangian continuum traffic flow models that are able to utilize trajectory information transmitted between connected vehicles via vehicle-to-everything (V2X) connectivity. These models capture three important features of traffic flow: (i) the propagation of congestions in time, (ii) the propagation of congestions in space, (iii) the string instability (or stability) of traffic that is related to the amplification (or decay) of traffic waves. The proposed models have only three tunable parameters to capture these three features. One of these parameters is the time delay that models the actuator lag in vehicle dynamics, the reaction time of human drivers, and the communication and feedback delays of connected and automated vehicles. The proposed Lagrangian continuum traffic models with delays establish a framework for traffic prediction and control. On one hand, connected vehicles may use predictions about the future motion of neighboring vehicles or their own. On the other hand, the continuum nature of these models allows one to study the large-scale impact of connected vehicles on the traffic flow. This opens the path for Lagrangian (vehicle-based) traffic control that supplements existing Eulerian (location-based) traffic control techniques.