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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,[email protected] Ad hoc linear networks.

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Zanella Andrea – Pierobon Gianfranco – Merlin Simone

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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,[email protected]

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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