# Risk of Collision and Detachment in Vehicle Platooning: Time-Delay-Induced Limitations and Trade-Offs (Extended Version)

## TL;DR

This paper analyzes the impact of communication delays and stochastic noise on vehicle platoon safety, providing explicit risk measures and revealing fundamental trade-offs between connectivity, delay, and risk.

## Contribution

It introduces closed-form risk expressions for vehicle platoons considering delays and noise, highlighting key limitations and trade-offs in network design.

## Key findings

- Higher network connectivity can reduce collision risk but may increase detachment risk.
- Time delay and stochastic noise jointly influence risk levels in complex ways.
- Explicit risk approximations enable better design of safer vehicle platoons.

## Abstract

We quantify the value-at-risk of inter-vehicle collision and detachment for a class of platoons, which are governed by second-order dynamics in presence of communication time-delay and exogenous stochastic noise. Closed-form expressions for the risk measures are obtained as functions of Laplacian eigen-spectrum as well as their fine explicit approximations using rational polynomial functions. We quantify several hard limits and fundamental tradeoffs among the risk measures, network connectivity, communication time-delay, and statistics of exogenous stochastic noise. Simultaneous presence of stochastic noise and time delay in a platoon imposes some idiosyncratic limitations on the behavior of collision and detachment risks, for instance, weakening (improving) network connectivity may result in lower (higher) levels of risk. Furthermore, a thorough risk analysis and comparison have been conducted for networks with specific graph topology. We support our theoretical findings via extensive simulations.