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Port-Hamiltonian systems are pertinent representations of many nonlinearphysical systems. In this article, we formulate and analyse a general class ofstochastic car-following models having a systematic port-Hamiltonian structure.The model class is a generalisation of classical car-following approaches,including the Optimal Velocity Model of Bando et al. (1995), the Full VelocityDifference Model of Jiang et al. (2001), and recent stochastic following modelsbased on the Ornstein-Uhlenbeck process. In contrast to traditional models forwhich the interaction is totally asymmetric (i.e., depending only on the speedand distance to the predecessor), the port-Hamiltonian car-following model alsodepends on the distance to the follower. We determine the exact stabilitycondition of the finite system with $N$ vehicles and periodic boundaries. Thestable system is ergodic with a unique Gaussian invariant measure. Otherproperties of the model are studied using numerical simulation. It turns outthat the Hamiltonian component improves the flow stability, reducing the totalenergy in the system. Furthermore, it prevents the problematic formation ofstop-and-go waves with oscillatory dynamics, even in the presence of stochasticperturbations.

Stability analysis of a stochastic port-Hamiltonian car-following model