We quantify the value-at-risk of inter-vehicle collision and detachment for a class of platoons, which are governed by secondorder 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 trade-offs 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 behavior risk of collision and detachment, for instance, weakening (improving) network connectivity may result in lower (higher) levels of risk. Furthermore, a thorough risk analysis is conducted for networks with specific graph topology. We support our theoretical findings via multiple simulations.

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For the class of noisy time-delay linear consensus networks, we obtain explicit formulas for risk of large fluctuations of a scalar observable as a function of Laplacian spectrum and its eigenvectors. It is shown that there is an intrinsic tradeoff between risk and effective resistance of the underlying coupling graph of the network. The main implication is that increasing network connectivity, increases the risk of large fluctuations. For vector-valued observables, we obtain computationally tractable lower and upper bounds for joint risk measures. Then, we study behavior of risk measures for networks with specific graph topologies and show how risk scales with network size. * The authors are with the

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