Randomized Algorithms for Data Propagation in Wireless Sensor Networks

Sotiris NikoletseasSotiris Nikoletseas

University of Patras (UoP) and (CTI), Greece.University of Patras (UoP) and (CTI), Greece.(visiting University of Geneva, Switzerland)(visiting University of Geneva, Switzerland)

COST/DYNAMO/GRAAL Meeting, Maribor, Slovenia, 2007

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Overview of the talkOverview of the talk

models / assumptionstwo problems: data propagation and energy balancethree representative protocols:

local optimization (LTP) probabilistic redundance (PFR) energy balance (EBP)

performance evaluation: analysis simulation

conclusions / more problems / future directions

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Work presented in this talk

- I. Chatzigiannakis, S. Nikoletseas and P. Spirakis, “Efficient and Robust Protocols for Local Detection and Propagation in Smart Dust Networks”, in the Journal of Mobile Networks (MONET), 2005.

- I. Chatzigiannakis, T. Dimitriou, S. Nikoletseas, and P. Spirakis, “A Probabilistic Algorithm for Efficient and Robust Data Propagation in Smart Dust Networks”, in the Journal of Ad-Hoc Networks, 2006.

- C. Efthymiou, S. Nikoletseas and J. Rolim, “Energy Balanced Data Propagation in Wireless Sensor Networks”, in the Wireless Networks (WINET) Journal, 2005.

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A Wireless Sensor Network• very large number of tiny “smart” sensors• severe limitations• densely / randomly deployed in an area• self-organization• co-operation• locality

an “ad-hoc” wireless network for:

• sensing crucial events• data propagation

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Unique characteristicsUnique characteristics

- - HugeHuge numbers, numbers, increased increased complexity, complexity, dense dense interactionsinteractions

- High- High dynamics dynamics / rapid/ rapid evolution evolution

- - AutonomicAutonomic character (open/self-organizing) character (open/self-organizing)

- - CooperationCooperation under severe constraints under severe constraints

- - LocalityLocality / lack of knowledge / lack of knowledge

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New Challenges (I)New Challenges (I)

- - Scalability:Scalability: how does protocol how does protocol performance/correctness scale with size?performance/correctness scale with size?

- - Efficiency:Efficiency: mainly energy, time mainly energy, time

- Fault-tolerance:- Fault-tolerance: can the network tolerate can the network tolerate

faults? To what extent?faults? To what extent?

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New Challenges (II)New Challenges (II)

Inherent trade-offs (e.g. energy vs time, fault-tolerance)Competing goals / various aspects:- minimizing total energy spent in the network- maximising the number of “alive” sensors over time- combining energy efficiency and fault-tolerance- balancing the energy dissipationApplication dependence

thusvariety of protocols needed / hybrid combinationsadaptive protocols, localitysimplicity, randomization, distributedness

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Limitations of Previous Work

Directed Diffusion: maintains a set of paths (e.g. a tree) to get data and reinforces best paths (it is suitable for low dynamics)

LEACH: sensors create clusters and elect cluster-heads that collect/aggregate/compress data and transmit directly to the control center

(it is suitable for small area networks)

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A smart dust “cloud” model A smart dust “cloud” model (a set of “particles” is spread in the plane)(a set of “particles” is spread in the plane)

Definitions: Let d the density of particles in the area.

Let R be the transmission range of each particle.

A receiving wall W is an infinite line in the plane. Sensor nodes

Sensor field

Control Center

The wall represents the authorities (the fixed control center).Alternatively, W may be a single point (the “sink” S). Each particle is aware of the location of W.

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The Problem of Local Detection and PropagationThe Problem of Local Detection and Propagation

A particle p detects a local crucial event ε

“How can particle p, via cooperation with the rest of the cloud, propagate information about event ε to the receiving wall W”

- Efficiency measures:

- propagation time (time for data to reach the control center)

- number of particle to particle transmissions (“hops”), which also characterizes energy consumption

- fault-tolerance

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Our Local Target Protocol (LTP)Our Local Target Protocol (LTP)

Let d(pi , pj ) the (vertical) distance of pi , pj and d(pi , W) the (vertical) distance of pi from W.

Each p’ receiving data does the following:

- Search Phase: It tries to discover a particle closer to W, i.e. a p’’ where d(p’’, W) < d(p’, W).

- Direct Transmission Phase: If found, then, p’ sends data to p’’

- Backtrack Phase: If repetitions of the search phase fail, then p’ sends data back to the particle it received data from.

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The search phase Example of a transmission

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Efficiency (number of hops)Efficiency (number of hops)

DefinitionsDefinitions: Let : Let hhopt opt the (optimal) number of “hops”the (optimal) number of “hops” ((vertical to vertical to WW transmissionstransmissions) needed to reach W, if ) needed to reach W, if particles always exist in distances particles always exist in distances RR towards towards WW..

Let Let hh the actual number of hops (transmissions) the actual number of hops (transmissions) taken to taken to reach reach WW. The . The “hops” efficiency“hops” efficiency of the protocol is: of the protocol is:

where where

opth h

hC

R

Wpdhopt

),(

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Simplifying Assumptions for a Rigorous Analysis

The position of p′′ is random uniform in the arc of angle 2α.

Each target selection is stochastically independent of the others.

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Theorem:Theorem: The The expected “hops” efficiencyexpected “hops” efficiency of the of the protocol in the protocol in the α-α-uniform case is uniform case is

Also Also

Proof:Proof: A A sequence of pointssequence of points is generated, is generated,

pp00 = p, p = p, p11, p, p22, …, p, …, ph-1h-1, p, phh

where where pph-1h-1 is within is within WW’s range and ’s range and pphh is beyond is beyond WW. .

Let Let ααii the anglethe angle of of ppii w.r.t. w.r.t. ppi-1i-1’s vertical line to ’s vertical line to WW. It is:. It is:

The The vertical progressvertical progress towards towards WW is is

sin)( hCE

57.12

)(1

hCE

h

iii

h

iii ppdWpdppd

11

1

11 ),( ),( ),(

iiii Rppd cos),( 1

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We get:

From Wald’s equation then

since

Assuming large values for hopt and since for it is

we get the result.

sin

2

1cos)(cos

a

ai dxxE

h

ii

h

iopti h

1

1

1

coscos

)(cos)()()(cos)1( iopti EhEhEEhE

2sin1

20

opth

opt hCE

h

hE 1

sin)(

)(

sin

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Summary evaluation of LTP

local, simple, greedy protocol

no global structure (set of paths) maintained

good for dense networks

performance drops in sparse / faulty networks

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- a protocol that avoids flooding by probabilistically favouring certain (“close to optimal”) data transmissions.

-Data is broadcast with probability

Pfwd = φ/π

while it is not propagated with probability 1- Pfwd.

- our protocol is very simple, uses only local information and assumes no co-ordination between sensors.

Our Probabilistic Forwarding Protocol (PFR)Our Probabilistic Forwarding Protocol (PFR)

S

E

1

2p1

p2

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The Correctness of PFRThe Correctness of PFR

Lemma: PFR Lemma: PFR always succeedsalways succeeds in sending in sending information from E to S information from E to S when the network is when the network is operationaloperational

In the proof, we use geometry (i.e. we cover the In the proof, we use geometry (i.e. we cover the network area by unit squares and show that network area by unit squares and show that there are always particles “close enough” to there are always particles “close enough” to the optimal line that always broadcastthe optimal line that always broadcast))

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The Energy Efficiency of PFR (I)The Energy Efficiency of PFR (I)

We consider We consider particles that propagate dataparticles that propagate data

as far as possibleas far as possible from ES line from ES line

We approximate We approximate ωω

by the following by the following random walkrandom walk::

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The Energy Efficiency of PFR (II)The Energy Efficiency of PFR (II)

By using By using stochastic dominancestochastic dominance by a continuous by a continuous time time “discouraged arrivals” birth and death “discouraged arrivals” birth and death processprocess, we prove:, we prove:

Theorem: The Theorem: The ratio of activated particlesratio of activated particles in PFR in PFR protocol is protocol is Θ((Θ((nn00/n)/n)22),), where n where n0 0 = |ES| and = |ES| and

nn22 = = NN is the number of particles in the is the number of particles in the network. For nnetwork. For n0 0 = o(n) this o(1). = o(n) this o(1).

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The Robustness of PFRThe Robustness of PFR

--We study the case when some of these particles We study the case when some of these particles are are not operatingnot operating

- - We consider particles We consider particles very near the ES linevery near the ES line

Lemma: PFR manages to propagate the Lemma: PFR manages to propagate the information across lines parallel to ES, and information across lines parallel to ES, and of of constant distance, with fixed nonzero constant distance, with fixed nonzero probabilityprobability..

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Experimental evaluationExperimental evaluation- Implementation of protocols: - software simulation (in ns2 + our extensions)

- real devices (Berkeley mica-1 motes)

- more realistic (technical details)- large scale (thousands of sensors simulated)- visualization of protocol evolution

- LTP/PFR comparison findings:

LTP is best is dense networks, while PFR is best in sparse networks.

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Our Energy Balance Protocol (EBP) - Motivation

Most protocols tend to “strain” some specific nodes in the network:

- In a hop-by-hop scheme the nodes closer to the sink tend to be overused.

- In a direct transmission scheme the distant nodes tend to be overused.

“How can we achieve equal energy dissipation per node in order to prolong the network lifetime by avoiding early network disconnection?”

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The Protocol

Data Propagation: Each node in sector i propagates messages as follows:- Propagate the message to sector i−1 with probabilty pi.- Propagate the message directly to the sink with probability 1−pi.The choice of pi is made such as the average per sensor energy dissipation is the same for all sensors in the network.

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Computation of pi (message handling)

Let hi the number of messages that handles sector i.

Let fi the number of messages that were forwarded to sector i.

Let gi the number of messages that were generated in sector i.

Clearly: hi = fi + gi

By linearity of expectation:

E[hi] = E[fi] + E[gi]

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A recurrence relation for pi

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A closed form A closed form for pi

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Dynamic aspects/HeterogeneityDynamic aspects/Heterogeneity

Two groups of nodesTwo groups of nodes: : - “usual” energy nodes- “usual” energy nodes- - super-nodessuper-nodes (twice as much energy) (twice as much energy)Same total energySame total energy as in the homogeneous case as in the homogeneous case(for fairness of comparison)(for fairness of comparison)Various heterogeneity degreesVarious heterogeneity degrees (20%-80% of total energy in super nodes)(20%-80% of total energy in super nodes)One more heterogeneity aspect: One more heterogeneity aspect: super-nodes super-nodes deployed in a non-uniform way (more nodes closer to the sink).

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Dynamic aspects/Dynamic aspects/RedeploymentRedeployment

We use the same number of nodes and separate them in g groups g0, g1, …. The group g0 is deployed at t = 0sec and each gi (for 0 < i < g) is deployed at t = i x 200sec.

We also examine the effect of non-uniform

redeployment for the nodes of groups g1, g2, … while the nodes of group g0 are always deployed uniformly.

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Adaptive/local exploration protocolsAdaptive/local exploration protocols

-The Adaptive Power Conservation Protocol (APCP) that locally and implicitly monitors the network conditions (density, energy) and accordingly adjusts towards good/optimal operation choices, in networks with node redeployment/heterogeneous sensors.

(I. Chatzigiannakis, A. Kinalis and S. Nikoletseas, in the Theory of Computing Systems (TOCS) Journal, 2007.)

- Fault-tolerant and Efficient Data Propagation using Limited, Local, Additional Network Information,

(I. Chatzigiannakis, A. Kinalis and S. Nikoletseas, in the Journal of Parallel and Distributed Computing (JPDC), 2007)

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Dynamic aspects/MobilityDynamic aspects/Mobility

Many, mobile sinks

We propose several sink mobility strategies for data collection that reduce energy a lot

(I. Chatzigiannakis, A. Kinalis and S. Nikoletseas, ACM MOBIWAC 06)

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Hybrid Worlds: A NanoPeers paradigmHybrid Worlds: A NanoPeers paradigm

• several similarities and differences of the two “worlds”…

• NanoPeers: a network of sensors acting as lightweight peers in a P2P overlay

• Hydrid layered models: several layers eg milli-peers coordinate micro-peers, micro-peers coordinate nano-peers, etc in the sense that higher order peers act as sinks for lower layers.

• an example application scenario: parcel delivery

- sensors (nano-peers) put on parcels- micro-peers put on boxes carrying several parcels- milli-peers put on (interconnected) warehouses

Goal: on-the-fly tracking of parcels

Thank youThank you!!