Suppressing secondary shock waves in jam-absorption driving via string-stable support vehicles

TL;DR

The study addresses secondary shock waves that arise when jam-absorption driving is used to clear a target shock on freeways. It introduces a string-stability-based support driving strategy that uses upstream support vehicles to extend time gaps and stabilize the high-density region, preventing secondary shocks. Using an IDM-based car-following model and a linear string-stability framework, the authors show that appropriate SD (with a large time gap) can achieve head-to-tail stability and suppress secondary waves, and they demonstrate the necessity of reverting extended gaps to reduce travel time. Remarkably, the results indicate that extremely low penetration of dedicated vehicles (a few SVs in a 2000-vehicle platoon) can yield safer, more fuel-efficient traffic with JAD, at the cost of modest travel-time increases.

Abstract

As a freeway-driving strategy, jam-absorption driving (JAD) clears a traffic shock wave (stop-and-go wave) by slowing down a single vehicle, called the absorbing vehicle. However, JAD may destabilize the traffic flow upstream of this vehicle, generating secondary shock waves. This study proposes a method to suppress secondary shock waves by controlling the behavior of connected and automated vehicles (CAVs) upstream of the absorbing vehicle, called support vehicles (SVs). A string-stability-based control method is applied in which SVs dynamically extend their time gaps to provide support driving (SD) for JAD. Numerical simulations revealed that SD damped perturbations caused by the absorbing vehicle and prevented secondary shock waves, consistent with the head-to-tail string stability criterion. Combining JAD and SD reduced fuel consumption and collision risk compared with the JAD-only method, but increased travel time. Reverting the extended time gap to its initial value reduced travel time while maintaining low collision risk compared with the non-reverting method, albeit with increased fuel consumption. Thus, combining JAD and SD effectively eliminates the target shock wave while suppressing secondary shock waves with guaranteed string stability.

Figures (8)

• Figure 1: (Left) Schematic of secondary waves in jam-absorption driving (JAD), composed of high-density region and secondary shock wave. The blue line indicates a single absorbing vehicle's spatiotemporal trajectory. (Right) Designs of JAD required for solving the secondary-wave problems. The scope of this study is to suppress the secondary shock wave by stabilizing the high-density region. To shrink and eliminate the high-density region is out of the scope of this study.
• Figure 2: Initial conditions of a single-lane system.
• Figure 3: (a) Velocity of the leading vehicle (vehicle 0) as a function of time $t$. (b) Schematic of the spatiotemporal trajectory of the absorbing vehicle.
• Figure 4: Gain characteristics. (a) Velocity-error transfer function. (b) Head-to-tail gap-error transfer function of platoon P in the supported state (Std-state). The thin black horizontal lines represent the vertical value of 1 as visual guides.
• Figure 5: (Left) Space-time and (Right) velocity-time diagrams. (a)--(b) No-control scenario. (c)--(d) JAD-only scenario. (e)--(f) JAD-Support scenario. $N_{\rm st} = 600$. (g)--(h) JAD-Support scenario. $N_{\rm st} = 200$. Space-time diagrams display vehicles 0, 50, 100, …, 1950 and 1999. Velocity-time diagrams display vehicles 800, 850, 900, …, 1950 and 1999. The absorbing vehicle (vehicle 800) and the support vehicles (SVs) are depicted by the blue and red lines, respectively, as visual guides. The vehicles upstream of the SV are depicted by the green lines in (e)--(f).