In critical alert services (e.g., a collision alert in a vehicular network) a message must reach all the recipients in a prespecified area within a maximum time, usually of few milliseconds, with guaranteed reliability. In this paper, we consider a Device-to-device (D2D)-enabled cellular network where User Equipments (UEs) use D2D transmissions to spread a message in their proximity, according to a centrally computed multihop schedule. Reception of D2D transmissions is probabilistic, with probabilities known a priori, e.g. based on the distance between two UEs. We want a given message to reach all the UEs in the network, within a maximum amount of time, with a pre-specified target probability. We show that the problem of computing: a) the minimal set of UEs that should initially possess the message to be disseminated, and b) the schedule that achieves the above objectives, is integer-non-convex, hence too complex to be solved optimally, and we propose a polynomial heuristic based on iterative decompositions, which always finds a feasible solution in negligible computation time. We analyze the performance of our scheme via simulation, showing that our centralized approach outperforms distributed ones relying on node cooperation, is considerably faster and requires far fewer transmissions.
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