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Zanella Andrea – Pierobon Gianfranco – Merlin Simone

Theorem. On the limiting performance of broadcast algorithms. over unidimensional ad-hoc networks. Zanella Andrea – Pierobon Gianfranco – Merlin Simone. Dept. of Information Engineering, University of Padova, {zanella,pierobon,merlo}@dei.unipd.it. Ad hoc linear networks.

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Zanella Andrea – Pierobon Gianfranco – Merlin Simone

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  1. Theorem On the limiting performance of broadcast algorithms over unidimensional ad-hoc networks Zanella Andrea – Pierobon Gianfranco – Merlin Simone Dept. of Information Engineering, University of Padova, {zanella,pierobon,merlo}@dei.unipd.it Ad hoc linear networks Optimum Broadcast strategy • Sensor networks • Car Networks • Limiting performance: • Minimum latency • Minimum traffic • Maximum reliability • minimized redundancy • preserved connectivity MCDS (Only nodes in a connected set of minimum cardinality rebroadcast packets) • Drawback: • Needed topologic information = Silent node = Transmitting node Linear nodes deployment modeled as an inhomogeneous Poisson arrivals Broadcast source x { } = MCDS s0 s2 s3 s4 s5 s6 s7 s8 s1 x x=0 Aim: mathematical characterization of the MCDS-broadcast propagation dynamic with inhomogeneous density of nodes Notations Hypothesis wk = distance reached by the k-th rebroadcast Pk = probability of the existence of the k-th rebroadcast fk (x ) = probability density function of wk, given that wk exists l(x ) = nodes density function • Ideal channel • Deterministic transmission radius (R) The dynamic of the MCDS-broadcast propagation along the network is statistically determined by the family of functions fk(x), which can be recursively obtained as follows: Example with a variable node density variable node density Connection probability as a function of distance and number of hops where Pk can, in turn, be recursively derived as p.d.f. of the front position weighted with the probability of its existence Homogeneous Case Connection Probability Asymptotic value* Number of reached nodes as a function of number of hops Number of hops * O. Dousse,et. al. “Connectivity in ad-hoc and hybrid networks”Proc. IEEE Infocom02 This work was supported by MIUR within the framework of the ”PRIMO” project FIRB RBNE018RFY (http://primo.ismb.it/firb/index.jsp).

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