Traffic Flow on a Ring With a Single Autonomous Vehicle: An Interconnected Stability Perspective

Giammarino, Vittorio; Baldi, Simone; Frasca, Paolo; Monache, Maria Laura Delle · 2020 · OpenAlex-citations

DOI: 10.1109/tits.2020.2985680

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Summary

This paper addresses the theoretical gap in understanding how a single autonomous vehicle (AV) can control traffic flow on a ring roadway, a setup used in field experiments to approximate infinite open roads. While experiments by Sugiyama et al. and Stern et al. demonstrated that human-driven vehicles (HVs) generate stop-and-go waves and that a single AV can dissipate them, existing theoretical frameworks relied heavily on classical asymptotic stability. These frameworks neglected "string instability," a phenomenon where disturbances amplify across vehicle interactions, which is prevalent in human driving behavior. The authors argue that standard string stability definitions are too restrictive for mixed traffic scenarios because they assume homogeneous dynamics and require non-amplification at every vehicle link, conditions that HVs inherently violate. To resolve this, the authors propose a new interconnected stability definition termed "weak ring stability" (WRS). Unlike strong ring stability, WRS allows for heterogeneous platoons and does not require the transfer function between adjacent vehicles to have an H-infinity norm less than or equal to one. Instead, it requires that the effect of a disturbance is not amplified as it propagates through the ring for a fixed number of vehicles. The study utilizes Linear Time-Invariant (LTI) systems theory, linearizing the nonlinear Optimal Velocity-Follow The Leader (OV-FTL) model for HVs around equilibrium. The authors derive a necessary and sufficient condition for classical stability for homogeneous HV rings, demonstrating that previously cited sufficient conditions are conservative, particularly for small numbers of vehicles. The paper analyzes mixed traffic scenarios containing HVs and a single AV. It proves a sufficient condition for the structural stability of such mixed platoons, showing that a single AV can stabilize any platoon size, though performance limitations exist for large platoons. The authors evaluate existing AV controllers, specifically a Proportional-Integral (PI) controller with saturation, finding that while it can stabilize the ring, it may not satisfy string stability requirements without reducing the sparsity of AVs. Numerical simulations using parameters from field experiments confirm that the proposed WRS framework explains the oscillatory phenomena observed in Sugiyama’s experiments (instability leading to stop-and-go waves) and Stern’s experiments (damping of waves). The significance of this work lies in providing a complete theoretical framework that combines classical and interconnected stability to explain experimental results. The introduction of weak ring stability clarifies the limitations of controlling traffic with sparse autonomous vehicles and offers a design procedure for AV controllers that can ensure string stability. This allows for the systematic design of AV behaviors that dampen oscillations, bridging the gap between empirical observations and theoretical control design in mixed traffic environments.

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• traffic density