Challenges for search in wireless networks

Gerhard HaßlingerSearch Methods inDynamic Wireless Networks

Challenges for search in wireless networks Random walks and flooding for search with partial info.

Evaluation using transient analysis and bounds

Efficiency of search methods in dynamic wireless networks Gerhard Haßlinger, T-Systems, Germany,

Thomas Kunz, Carleton University, Ottawa, Canada,E-Mail: [email protected], [email protected]


Queue Length Knowledge Age Inaccuracy Level

0

2

4

6

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10

12

14

16

Knowledge Age [s]

Inac

cura

cy L

evel

[pac

kets

]

1.000.500.220.140.10

Traffic Rate

Experience with wireless routing:Inaccuracy of node state info.

for OLSR routing (RFC 3626)

OLSR information enhanced by probing

Traffic

Rate

% Know- ledge

Updates

Mean Age: Improvement

by Probing

0.10 36% 4.8s 2.13s

0.14 42% 5.6s 2.66s

0.22 54% 7.3s 3.63s

0.50 30% 9.7s 5.47s

1.00 15% 11.1s 6.5s

NS2 Simulation Parameters

Network Type IEEE 802.11

Propagation Model TwoRayGround

Transmission Range 250 m

Topology 50 nodes, random locations in 1 km2

Mobility Model static

Simulation Time 200s

Queue TailDrop, 50 Pct


No full support for routing and search can be given in Wireless and mobile networks Sensor networks Overlay, peer-to-peer networks

Advantage: More flexibility to set up and expand networks,

less overhead in managing networks with high churn

Disadvantage: More expensive search by exploration of the network

The Internet itself exhibits unstructured growth and churn, but the IETF (Cisco, Juniper ...) established reliable routing and search engines (Google, Yahoo, …) provide content exploration New IETF WG on “Routing for low power & lossy Networks”

Challenges for search in wireless networks


Network exploration by flooding & random walks

Flooding is exhaustive for all neighbors up to a distance d or time to live (TTL); Parallel search; large amount of messages spread in all directions

Random walks follow some probabilistic winding route


Control of message overhead for flooding is difficult: Unknown network coverage as a function of the distance d Coverage may rise e.g. from 3% to 30% in one step d d + 1

A random walk of predefined length L has fixed expense Randoms walks can proceed in parallel, with forking or can be enhanced by flooding with small d from some points Many ways to combine random walks & flooding schemes (see Gkantsidis et al., IEEE Infocom 2004 & ’05) Network coverage is partial, but random walk searches are efficient e.g. for replicated data in P2P networks Random network growth is also efficiently supported by r. walks

Network exploration by flooding & random walks


Transient analysis of basic random walks

Performance studies on random walks prefer simulation,although transient analysis offers a simple and scalable alternative

Bounds e.g. based on second largest eigenvalue of the transition matrix prove convergence but often are not tight

Performance criteria: Number of steps required - to reach a target node - or for network coveragewith predefined probability (e.g. 99%)

Transient analysis - computes the probability distribution for the random walks’ sojourn node step by step - starting from a node or an arbitrary initial distribution


Basic transient analysis of a random walks

An absorbing state („black hole“) is introduced at a considered network node

The probability to enter the absorbing state from some starting conditions, e.g. from steady state, equals the probability to discover the network node during the random walk

For networks with heterogeneous nodes, coverage can be studied depending on different types or degrees of nodes


Example of a transient random walk analysis

Absorbing state: Modified graph for considering a target

1. hop

...

Start 2. hop 12. hop: 10.11% 10%

14.89% 15%

20.23% 20%


Performance Results for random walk & flooding

0

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2 4 6 8 10 12 14 16 18 20

Distance from source to target node over grid diagonal

Nu

mb

er o

f ra

nd

om w

alk

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ps

for

99%

su

cces

s

20% Routing info for 30% Routing info Random 50% Routing info Walks 70% Routing info 90% Routing infoFlooding messages to distance

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160

200

2 4 6 8 10 12 14 16 18 20

Distance from source to target node over grid diagonal

Nu

mb

er o

f ra

nd

om w

alk

ste

ps

for

90%

su

cces

s

20% Routing info for 30% Routing info Random 50% Routing info Walks 70% Routing info 90% Routing infoFlooding messages to distance

Random walks: Number of hops required for 90% and 99% success

for different levels of available routing info and for different distances to destination (up to 20 hops on a grid diagonal)


Extensions of the transient analysis for random walks

The following cases are tractable by extended analysis:

- Several random walks in parallel product formula for the probability that independent trials miss a node

- Random walk without step back (except for nodes of degree 1) increased state space for analysis: network edges instead of nodes, but the run time complexity is unchanged

- Random walk followed by flooding on distance d after the last step extend absorbing state to the set of all neighbors up to distance d

- Random walk search for replicated data on n nodes use a set of n absorbing states or assume a binomial distributed hit count based on single node search


m: Distance to the destination after m random walk steps (with changes)

m has a binomial distribution:

for unrestricted range of distances in both directions

with mean E(m) = –m (q–p)/(q+p); variance 2(m) = mpq/(q+p)

if m(q–p)/(q+p) > E(m) < 0 destination is reached with > 50%

Start

p q

D:023 1 -1 -3-2S:

p qDestination

kmk

m qp

p

qp

qkm

km

}2Pr{

Convergence bound for biased random walks

D:0

S:

Example:2-dim.Grid


Bound (thin lines) compared to transient analysis

0

40

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2 4 6 8 10 12 14 16 18 20

Distance from source to destination node over grid diagonal

Res

ult

: tr

an

sien

t a

na

lysi

s a

nd

bo

un

d (

90

% s

ucc

ess)

. .

20% Routing Info Available 30% 50% (Bounds as thin, 70% almost parallel lines) 90% Flooding messages to distance" "Reihe8Reihe9Reihe10Reihe11


Conclusions

Random walks are useful for search and routing in networks with unreliable or incomplete information on target nodes

Random walks outperform flooding for large hop distances

Many options for combining routing, flooding & random walks for improved performance in different scenarios

Transient analysis yields accurate evaluation of random walks - for the basic case and many variants - is scalable for networks of large size - bounds can be given on convergence behaviour

Challenges for search in wireless networks

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