1 A Novel Capacity Analysis for Wireless Backhaul Mesh Networks Tein-Yaw David Chung, Kung-Chun Lee, and Hsiao-Chih George Lee Department of Computer Science and Engineering Yuan Ze University, Taiwan, R.O.C. April 1, 2008
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A Novel Capacity Analysis for Wireless Backhaul Mesh Networks
Tein-Yaw David Chung, Kung-Chun Lee, and Hsiao-Chih George Lee
Department of Computer Science and Engineering Yuan Ze University, Taiwan, R.O.C.
April 1, 2008
Abstract
• Primary design goal– To find an analytic method
to determine the capacity upper bound for network planning of wireless backhaul mesh networks
2
3
Outline1. INTRODUCTION
2. RELATED WORK
3. SYSTEM MODEL
4. ANALYTIC ANALYSISAND SIMULATION RESULTS
5. CONCLUSION AND FUTURE WORK
Inter-flowIntra-flow
InternetInternetWireless MeshBackhaul
WiFi NetworksCellular Networks
Wireless Mesh LinkOther type of link
SSSS
SSSS
MeshClient
MeshClient
Mesh Client
SS
BS
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INTRODUCTION
• Architecture of Wireless Mesh Networks (WMNs)– Subscriber Station (SS)
– Base Station (BS)
– Mesh Client
• Traffic on the backhaul– Multi-hop forwarding
– Intra-flow & inter-flow
Inter-flowIntra-flow
Inter-flowIntra-flow
InternetInternetWireless MeshBackhaul
WiFi NetworksCellular Networks
Wireless Mesh LinkOther type of link
SSSS
SSSS
MeshClient
MeshClient
Mesh Client
SS
BS
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Wireless Mesh Network (WMN)
• Scheduling– Centralized vs.
distributed
• Transmission– Time Division Duplex
(TDD ) vs. Frequency Division Duplex (FDD)
Question: Capacity upper bound for inter-flow in centralized-control TDD-based WMNs
Inter-flow
RELATED WORK
• Bottleneck Collision Domain (BCD) [7] – Distributed
– Pessimistic
– Need simulation
Bottleneck Collision Area (BCA)– Centralized
– Optimistic Tighter upper bound
– A closed-from expression Analytic Readily used
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[7] J. Jun and M.L. Sichitiu, “The Nominal Capacity of Wireless Networks”
No overflow
No contentionNo error
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SYSTEM MODEL • Assumptions
– Transmission• Single channel, single-radio (SC-SR)• Omni-directional antenna• Fixed transmission power * • Single-rate transmission *• Interference model: Protocol model [2]
– Traffic Pattern• Equal downlink and uplink inter-flows per node• Shortest path routing
– MAC scheme• Symmetric MACA
[2] P. Gupta and P.R. Kumar, ``The Capacity of Wireless Networks."
Network Model
• Network nodes – Infinity
number of nodes *
– Uniformly distributed
• Centralizedscheduling
• TDD (Time Division Duplex)
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Inter-flowIntra-flow
InternetInternetWireless MeshBackhaul
WiFi NetworksCellular Networks
Wireless Mesh LinkOther type of link
SSSS
SSSS
MeshClient
MeshClient
Mesh Client
SS
BS
Scheduling-Based Method
• Period of schedule ε: (1)
• Throughput over link l with schedule ε is
(2)
where |εl| = number of timeslots assigned to εl W = channel capacity
• Per-node capacity with schedule ε
(3)
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( ) max maxll L t
Period t
number of timeslot on ( , )
period of ( )llink l
l W WPeriod
2
( )
W
Period
Ring-based Network Model
Fig. 1 Diagram of a ring-based network and various collision areas10
Ring 1
Ring 2
Ring 3
Ring 4
BS
dreuse
collision area
bottleneck collision area
Inter-flow linkInter-flow link in collision domainSS
3-hop node
2-hop node
1-hop node
1-hop link
2-hop link
3-hop link
(i,j)
(u,v)
< dreuse
• Distance between two links – The maximum distance between their terminal nodes
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DCBA
d(A, D)
A
B
D
C
d(A, D)
[Case 1] Two p-links on a line [Case 2] Two p-links not on a line
• Minimum reuse distance, dreuse
– [Case 1] Two p-links on a line
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D
fp p
CB
dreuse = 2p + f
A
– [Case 2] Two p-links not on a line
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f
p
A
B
D
pC
dreuse < 2p + f
<p+f
<2p+f
• Collision area (CA) – An area in which no any two links can transmit
simultaneously
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Ring 1
Ring 2
Ring 3
Ring 4
BS
dreuse
collision area
bottleneck collision area
Inter-flow linkInter-flow link in collision domainSS
3-hop node
2-hop node
1-hop node
1-hop link
2-hop link
3-hop link
(i,j)
(u,v)
< dreuse
• Maximal collision area– Two p-links on a line
– The circle with diameter dreuse
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D
fp p
CB
dreuse = 2p + f
A x
H
G
F
E
[Case 2] two p-links not on a line[Case 1] two p-
links on a line
• Bottleneck collision area (BCA) – CA with the maximum traffic load.
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Ring 1
Ring 2
Ring 3
Ring 4
BS
dreuse
collision area
bottleneck collision area
Inter-flow linkInter-flow link in collision domainSS
3-hop node
2-hop node
1-hop node
1-hop link
2-hop link
3-hop link
(i,j)
(u,v)
< dreuse
ANALYTICAL ANALYSIS• Per-node capacity upper bound:
(12)
where n = number of SSs = density of SSs
p = transmission range
d = radius of the network
W = channel capacity 17
2
2 1
2
2 1 1
1
/
11,
31
/ 2 , reuse
W WO
n nc c p d
xc c c
x d p p d
• For MC-MR WMNs, given n = number of nodes
= per-node capacity
c = number of non-overlapping channels
m = number of radios per node
through a proper channel assignment:– maximum per-node capacity =
– maximum network capacity =
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n c
1 m c n
c
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Per
node c
apaci
ty
Transmission range (km)
d=0.4 (km)d=0.7 (km)d=1.0 (km)d=1.3 (km)
19Fig. 3 Per-node capacity with various p, where and n = 100.0.5
21%
3%
20
0.4
0.5
0.6
0.7
0.8
0.9
1
10 20 30 40 50 60 70 80 90 100
Number of SSs, n
p=0.4(km)
Total capacity
p=0.7(km)p=1.0(km)p=1.3(km)
Fig. 4 Total capacity with various n, where and d = 1km.0.5
SIMULATION RESULTS
• Compare– BCA
– BCD [7]
– Linear programming algorithm [4]
[4] M. Kodialam and T. Nandagopal, “On the Capacity Region of Multi-Radio Multi-Channel Wireless Networks”
[7] J. Jun and M.L. Sichitiu, “The Nominal Capacity of Wireless Networks”
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0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Transmission range, p (km)
BCA (Analysis)Algorithm in [4] (Simulation)BCD (Simulation)
Per-node capacity
Fig. 5 Per-node capacity with various p, where , n = 100, d=1 km0.5
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0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
60 80 100 120 140 160 180 200
Number of SSs, n
Algorithm in [4] (Simulation)BCA (Analysis)
BCD (Simulation)
Total capacity
Fig. 6 Total capacity with various n, where , p = 1, and d = 0.5 km.0.5
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CONCLUSION• Bottleneck Collision Area (BCA)
– Analytic analysis– Closed-form expression – Tighter capacity upper bound
• Much larger than that of the BCD [7]• Close to linear programming algorithm [4]
p
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FUTUR WORK
• Finite node density• Non-uniform transmission power• Multi-rate transmission
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Thank you !
Q & A
Q&A
• Analytical (BCD)– Per-node capacity: (p) Asymmetric vs. Symmetric – Per-node capacity: (d) Asymmetric vs. Symmetric
• Simulation (BCD, Algorithm [4], and BCD [7]– Per-node capacity: vs. – Per-node capacity: (p) Asymmetric vs. Symmetric – Per-node capacity: (n) Asymmetric vs. Symmetric
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1.0 0.5
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