Piecewise-linear car-following with heterogeneous agent dynamics: Consensus and emerging collective behaviors

The dynamics of multiples agents with heterogeneous behaviors, and under constraints on speed limits and safe separation distances are generally nonlinear and complex. A deep comprehension of such dynamics, in particular the derivation of eventual emerging collective behaviors would open the doors for a deep understanding of the physics of such systems, and then for the optimization and optimal control of the agent dynamics and of the macroscopic behaviors, with possible interesting applications in multiple fields, such as autonomous driving, unmanned air vehicles, etc. We present in this article an extension of an existing car-following model where a number of agents move on a ring without passing and with constraints on agents’ speed limits and safe separation. The extension includes the possibility to consider heterogeneous behaviors of the agents, contrary to the existing model which is limited to homogeneous behaviors. We analyze the agent dynamics and characterize the conditions under which stationary regimes exist. Moreover, we analytically derive the asymptotic characteristics of the system. In particular, we analytically derive the average asymptotic agent-speed as a function of the total agent-density in the ring, and of the different agent-behaviors considered. Furthermore, we show that collective behaviors emerge and characterize them under different conditions.