A Critical Packet‐Loss Threshold for Collisions in Cooperative Vehicle Platoons: Speed Invariance, Finite‐Size Scaling and a Burst‐Exceedance Theory

Cooperative adaptive cruise control (CACC) enables vehicle platoons to maintain short, stable intervehicle gaps through vehicle‐to‐vehicle (V2V) communication, which makes their safety dependent on packet loss. This study treats platoon collisions as a critical phenomenon, with crash probability as an order parameter and packet delivery ratio (PDR) as a control parameter. Coupled network and traffic simulations of an eight‐vehicle platoon operating under the partners for advanced transportation technology (PATH) cooperative control law reveal, under 0.2 Hz sinusoidal disturbances, a sharp critical threshold at a PDR of 0.386 ± 0.008, below which collisions become likely. The transition width is 0.026, and the result is robust to the choice of crash‐gap criterion. For this constant‐spacing controller, the threshold varies by less than 0.3% over a 70 km per hour range of cruise speeds; a second controller with a constant‐time‐headway policy shows the same sharp transition, with a threshold set mainly by its equilibrium gap. The threshold rises and the transition narrows with platoon size, with a fitted width exponent of −0.51 (95% confidence interval −0.93 to −0.18), consistent with the order‐statistics value of −1/2. A closed‐form burst‐exceedance model based on Poisson statistics reproduces the simulated sinusoidal threshold with a single calibration offset. Extended to the Gilbert–Elliott (GE) burst‐correlated channel, it shows that the independent‐loss assumption common in control studies is strongly nonconservative: for a moderate mean burst length of five packets, the required PDR of this platoon rises from 0.39 to 0.95 analytically and to 0.97 in network simulations. The results map measured channel statistics to safety‐critical delivery requirements for CACC platoons.