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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]. Challenges for search in wireless networks - PowerPoint PPT Presentation
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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]
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
Queue Length Knowledge Age Inaccuracy Level
0
2
4
6
8
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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
Gerhard HaßlingerSearch Methods inDynamic 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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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%
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
Performance Results for random walk & flooding
0
50
100
150
200
250
300
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
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
0
40
80
120
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)
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
Bound (thin lines) compared to transient analysis
0
40
80
120
160
200
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
Gerhard HaßlingerSearch Methods inDynamic Wireless Networks
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