Zanella Andrea – Pierobon Gianfranco – Merlin Simone

1. 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) Theorem 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: Performance metrics Ck(x) = Connection probability of x in k hops NkC= Mean number of nodes reached in k hop Results: Connection probability, Propagation statistics, … where Pk can, in turn, be recursively derived as 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 Inhomogeneous (general) Case Homogeneous Case Example: nodes reached at each hop Connection Probability Asymp. value* Number of hops variable node density * 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).