10/24-10/27.2004mwcn 20041 theoretical capacity of multi-hop wireless ad hoc networks yue fang...
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10/24-10/27.2004 MWCN 2004 1
Theoretical Capacity of Multi-hop Wireless Ad Hoc Networks
Yue Fang
A.Bruce McDonald
R-WIN Lab
ECE Department
Northeastern University
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Outline
Introduction Network Saturation Capacity Maximum Instantaneous Capacity Discussion
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Outline
Introduction Network Saturation Capacity Maximum Instantaneous Capacity Discussion
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Wireless Ad Hoc Networks
Easy to setup, no wiring required Provides support of mobile (and ubiquitious)
computing Limited resources Lower capacity Dynamic characteristics
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Capacity Analysis of Wireless Ad Hoc Networks
The capacity of wireless network (Gupta & Kumar)
Theoretical maximum throughput of 802.11 Channel capacity of multi-hop wireless ad
hoc network
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Network Capacity
Network Capacity The ability of data exchange the whole network can bear
at any time. No universal semantic is available. Two interpretations of network capacity
Maximum instantaneous capacity (MIC) • Ideal routing and scheduling
Network saturation capacity (NSC)• Uniformly distributed nodes and traffic independent of
routing and scheduling.
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Topology Generation
Network topology is generated by repeating specific patterns to avoid unnecessary randomness.
nnavgavg=3=3 nnavgavg=6=6
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Outline
Introduction Network Saturation Capacity Maximum Instantaneous Capacity Discussion
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Previous Work
Novel concepts --- “deferral set” and “equivalent competitor” are proposed to facilitate multi-hop capacity analysis. Deferral set: the set of all nodes and links that will affect
the ongoing communication Equivalent Competitor: The amount of competition faced
by the ongoing communication in terms of single node.
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Previous Work (2) Node being two hop neighbor
depends on whether it has a neighbor which is direct neighbor of ongoing communication.
Only the communication from two hop neighbor to one hop neighbor will affect the ongoing communication.
Channel capacity (Schan) is derived based on node behavior model.
F
I
G
H
A
C E
D
B
Only communication between C and F will affect the communication between A and B, thus the equivalent competitor is 1/3.
X
X
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Network Saturation Capacity (NSC)
It is necessary to study the relation between the capacity and node location.
navg N NSC(Mb/s) navg N NSC(Mb/s)
Nl x Schan
Sim-ulation
Nl x Schan
Sim-ulation
3 49 1.75 1.779 4 64 1.56 1.636
6 81 1.06 1.52 8 81 0.957 1.17
11 75 0.417 0.86 12 81 0.405 0.82
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Boundary Condition Nodes that close to the boundary of the network
have fewer neighbors. Hence less channel contention, consequently, greater available capacity.
Boundary zone is defined as the doughnut shaped region occupied by all nodes that are more closer to the boundary (Xi < 2r, where Xi is the distance from node i to the network boundary).
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Phantom Node Nodes in the boundary zone
(A, B) tend to have higher capacity than the nodes in the center of the network.
Nodes in the shaded area are called “phantom” nodes
In order to have an accurate estimation of network saturation capacity, the percentage of “phantom node” to the number of nodes in the network should below a threshold.
AA
BB2r-d2r-d
dd
αα
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NSC: How big is big?
Boundary condition effect can be regarded as negligible when then network radius is at least 10 times of transmission range.
Additional parameters may affect network capacity: such as spatial and temporal variation of distribution of nodes, traffic, channel quality, mobility, etc.
Number of phantom nodes vs. Number of phantom nodes vs. R/rR/r
Percentage of phantom nodes Percentage of phantom nodes to Numto Num
Num
ber
of P
hant
om N
odes
# of
pha
ntom
nod
es/ t
otal
nod
es
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Outline
Introduction Network Saturation Capacity Maximum Instantaneous Capacity Discussion
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Maximum Instantaneous Capacity (MIC)
MIC reflects the bottleneck throughput between any set of sources and destinations.
MIC can only be achieved under ideal scheduling --- every link either transmitting/receiving, or in deferral state.
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Maximum Instantaneous Capacity (MIC)
The objective is to find a sequence of simultaneously active links --- aggregate link set that cover the connected work. MIC is the bottleneck of the aggregate link set.
MIC can be approximated in two steps: Find the maximum aggregate link set --- NP
problem Find the bottleneck
c1 simultaneous c1 simultaneous linkslinks
c2 simultaneous c2 simultaneous linkslinks
c3 simultaneous c3 simultaneous linkslinksc1>= c2>=c3c1>= c2>=c3
Bottleneck Bottleneck is the MIC: is the MIC:
c3c3
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44
11
22
33 55
NP completeness By appropriate means, the problem of finding maximum aggregate
link set in the network can be transformed to classic maximum independent set problem [6].
(1,2(1,2))
(4.5(4.5))
(3,4(3,4))
(2,5(2,5))
(2,3(2,3))
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MIC: The greedy Algorithm
1. List all the feasible deferral sets in ascending order by the number of links in each set.
2. Pick the first deferral set in the list , transmission along corresponding link can be granted.
3. If more than one deferral set have same size, the tie is broken by activating the link with minimum LOS (line-of-sight) distance.
4. Update the candidate deferral list.
5. Update the size of remaining feasible deferral sets.
6. Repeat 1-5 until the candidate deferral set list is empty.
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Random Link Selection
Randomly select the link to be activated. Faster than greedy heuristic Results are of the same order.
N Concurrent Links
Greedy Random
432 3 118 99
530 4 119 87
737 6 139 108
952 8 163 115
nnavgavg
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Bottleneck Aggregate Link Set
Every link has to be activate at least once. The MIC is the bottleneck the maximum aggregate link
set. The optimal solution is NP-complete. Greedy algorithm has polynomial bounded number of
iterations. Random selection.
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Experimental Result
N Greedy Algorithm Random Selection
Round Bottleneck Round Bottleneck
432 3 116 111 45 94
530 4 241 110 95 82
737 6 591 128 178 101
952 8 1899 152 348 107
nnavgavg
Number of requited iterations and corresponding lower bound
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Outline
Introduction Network Saturation Capacity Maximum Instantaneous Capacity Discussion
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Discussion The semantic of network capacity itself is analyzed to
provide a clearer understanding and basis for comparison. The analysis is central of a broad cross-layer framework Extensible in terms of access protocols, generalization and
application to real control problems. The results, while sub-optimal and on worst-case analysis
improve on the most often cited results from [2]
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Discussion (2) From [2], using protocol model, the capacity of a random
network is Number of concurrent active link in a saturated network
can be approximated by the number of non-overlapping level-1 interference sets. Which can be obtained by:
Network capacity then is:
(lo g
)W
n n
R
r
N
nr
r
N
navg
avg
2
2
2
20 9 8
1
0 9 8 0 9 8 1( . ) ( . ) ( . ) ( )
1 '
/ / 2 ( 1)avg
avg avg
NC W
n C W
N n N N n
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Conclusion
The extension of the channel capacity analysis [?] The semantic of network capacity is discussed with two
interpretation --- NSC and MIC. Agreement of the results reported in [2] mutually
validated the two models Provides insight regarding how to more effectively
leverage available network capacity.
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Reference
[1] “Theoretical channel capacity in multi-hop ad hoc networks” by Yue Fang and A. Bruce McDonald
[2] “ The capacity of wireless networks’’ by P. Gupta and P.R. Kumar
[3] “Finding a maximum independent set” by R. E. Tarjan and A. E. Trojanowski.
[4] “Theoretical Maximum Throughput of IEEE 802.11 and its Applications” by Jangeun Jun, Pushkin Peddabachagari and Miail Sichitiu