From homogeneous to heterogeneous traffic flows: Lp String stability under uncertain model parameters

This paper shows that the heterogeneity of drivers’ and vehicles characteristics makes platoons, on average, more string-unstable. However, the string instability degree of unstable platoons is much higher in a homogeneous flow than in a heterogeneous one. These results are based on an L∞ characterization of string stability, which is shown to be the most appropriate one from a traffic safety viewpoint. Mechanisms and conditions are discussed in which an L2 characterization is not able to capture the amplification of a speed drop through a string of vehicles. An analytical sufficient condition for the L∞ string stability of heterogeneous vehicles, which move according to a general class of car-following models, is derived. Above all, a thorough comparison of L∞ and L2 string stability characterizations between a homogeneous and a heterogenous flow, is performed. To this aim, the Lp norms of heterogeneous platoons are calculated within a quasi-Monte Carlo framework. The variability of the Lp norm values due to the platoon length, the equilibrium speed, and the probability distribution model of the uncertain vehicle parameters, is analysed. Overall, it is shown that the platoon stability behaviour sensibly changes with the shape and the correlation structure of vehicle model parameter distributions. Therefore, traffic heterogeneity needs to be modelled in order to correctly characterize the string stability of a mixed traffic flow.