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

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

4

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

5

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

6

[7] J. Jun and M.L. Sichitiu, “The Nominal Capacity of Wireless Networks”

No overflow

No contentionNo error

7

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)

8

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)

9

( ) 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

11

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

12

D

fp p

CB

dreuse = 2p + f

A

– [Case 2] Two p-links not on a line

13

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

14

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

15

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.

16

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 =

18

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”

21

22

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

23

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

24

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

25

FUTUR WORK

• Finite node density• Non-uniform transmission power• Multi-rate transmission

25

26

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

27

1.0 0.5

28

Reference1. I.F. Akyildiz and X. Wang,“A Survey on Wireless Mesh Networks,” IEEE Communications Magazine, vol. 43, Issue 9, September

2005.

2. P. Gupta and P.R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions on Information Theory, March 2000.

3. P. Kyasanur and N.H. Vaidya,“Capacity of Multi-Channel Wireless Networks: Impact of Number of Channels and Interfaces,” ACM Mobicom, August 2005.

4. M. Kodialam and T. Nandagopal, “Characterizing the Capacity Region in Multi-Radio Multi-Channel Wireless Mesh Networks,” ACM Mobicom, August 2005.

5. M. Kodialam and T. Nandagopal, “On the Capacity Region of Multi-Radio Multi-Channel Wireless Mesh Networks,” IEEE Workshop on Wireless Mesh Networks (WiMesh), September 2005.

6. W. Wang and X. Liu, “A Framework for Maximum Capacity in Multi-channel Multi-radio Wireless Networks,” IEEE Consumer Communications and Networking Conference, 2006.

7. J. Jun and M.L. Sichitiu, “The Nominal Capacity of Wireless Mesh Networks,” IEEE Wireless Communications Magazine, vol. 10, October 2003.

8. M. Malekesmaeili, M. Shiva, M. Soltan, “Topology Optimization for Backbone Wireless Mesh Networks,” Fifth Annual Conference on Communication Networks and Services Research, 2007.

9. X. Wu, J. Liu, and G. Chen, “Analysis of Bottleneck Delay and Throughput in Wireless Mesh Networks,” IEEE International Conference on Mobile Ad-hoc and Sensor Systems, 2006.

10. E. Miorando and F. Granelli, “On Connectivity and Capacity of Wireless Mesh Networks,” IEEE International Conference on Communications, 2007.

11. J. Huang, L. Wang, and C. Chang, "Coverage and capacity of a wireless mesh network," International Conference on Wireless Networks, Communications and Mobile Computing, vol. 1, June 2005.

12. J. Huang, L. Wang and C. Chang, "Capacity and QoS for a scalable ring-based wireless mesh network," IEEE JSAC, vol. 24, November 2006.

13. G. Mergen and L. Tong, “Stability and Capacity of Regular Wireless Networks,” IEEE Transactions on Information Theory, June 2005.