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Zanella Andrea – Pierobon Gianfranco – Merlin Simone Ad hoc linear networks Sensor networks Car Networks Optimum Broadcast strategy MCDS (Only nodes in a connected set of minimum cardinality rebroadcast packets) ‏ Linear nodes deployment modeled as an inhomogeneous Poisson arrivals minimized redundancy preserved connectivity Limiting performance: Minimum latency Minimum traffic Maximum reliability Drawback: Needed topologic information x=0 x s0s0s0s0 s1s1s1s1 s2s2s2s2 s8s8s8s8 s5s5s5s5 s6s6s6s6 s7s7s7s7 s3s3s3s3 s4s4s4s4 x { } = MCDS Broadcast source = Silent node = Transmitting node Dept. of Information Engineering, University of Padova, This work was supported by MIUR within the framework of the ”PRIMO” project FIRB RBNE018RFY ( Ideal channel Deterministic transmission radius (R) ‏ Hypothesis Notations w k = distance reached by the k-th rebroadcast P k = probability of the existence of the k-th rebroadcast f k (x ) = probability density function of w k, given that w k exists  (x ) = nodes density function Aim: mathematical characterization of the MCDS-broadcast propagation dynamic with inhomogeneous density of nodes The dynamic of the MCDS-broadcast propagation along the network is statistically determined by the family of functions f k (x), which can be recursively obtained as follows: Theorem where P k can, in turn, be recursively derived as * O. Dousse,et. al. “Connectivity in ad-hoc and hybrid networks” Proc. IEEE Infocom02 Example: nodes reached at each hop Homogeneous Case Results: Connection probability, Propagation statistics, … variable node density Inhomogeneous (general) Case Asymp. value* Connection Probability Number of hops Performance metrics C k (x) = Connection probability of x in k hops N k C = Mean number of nodes reached in k hop