  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.
