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Aim: mathematical characterization of the MCDS-broadcast propagation dynamic with inhomogeneous density of nodes. Notations. Hypothesis. w k = distance reached by the k -th rebroadcast P k = probability of the existence of the k -th rebroadcast

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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).


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