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 Outline 1.INTRODUCTION 2.RELATED WORK 3.SYSTEM MODEL 4.ANALYTIC ANALYSIS AND SIMULATION RESULTS 5.CONCLUSION AND FUTURE WORK

Inter-flow Intra-flow Internet Wireless Mesh Backhaul WiFi Networks Cellular Networks Wireless Mesh Link Other type of link SS Mesh Client Mesh Client 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-flow Intra-flow

Inter-flow Intra-flow Internet Wireless Mesh Backhaul WiFi Networks Cellular Networks Wireless Mesh Link Other type of link SS Mesh Client Mesh Client 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 contention No 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 Centralized scheduling TDD (Time Division Duplex) 8 Inter-flow Intra-flow Internet Wireless Mesh Backhaul WiFi Networks Cellular Networks Wireless Mesh Link Other type of link SS Mesh Client Mesh Client Mesh Client SS BS

Scheduling-Based Method Period of schedule ε: (1) Throughput over link l with schedule ε is (2) where |ε l | = number of timeslots assigned to ε l W = channel capacity Per-node capacity with schedule ε (3) 9 

Ring-based Network Model Fig. 1Diagram of a ring-based network and various collision areas 10

Distance between two links –The maximum distance between their terminal nodes  11 [Case 1] Two p-links on a line[Case 2] Two p-links not on a line

Minimum reuse distance, d reuse –[Case 1] Two p-links on a line 12

–[Case 2] Two p-links not on a line 13

Collision area (CA) –An area in which no any two links can transmit simultaneously  14

Maximal collision area –Two p-links on a line –The circle with diameter d reuse 15 [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

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

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

19 Fig. 3Per-node capacity with various p, where and n = % 3%

20 Fig. 4 Total capacity with various n, where and d = 1km.

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 Fig. 5 Per-node capacity with various p, where, n = 100, d=1 km

23 Fig. 6 Total capacity with various n, where, p = 1, and d = 0.5 km.

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

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

28 Reference 1.I.F. Akyildiz and X. Wang,“A Survey on Wireless Mesh Networks,” IEEE Communications Magazine, vol. 43, Issue 9, September 2005.I.F. Akyildiz and X. Wang 2.P. Gupta and P.R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions on Information Theory, March 2000.P. Gupta and P.R. Kumar 3.P. Kyasanur and N.H. Vaidya,“Capacity of Multi-Channel Wireless Networks: Impact of Number of Channels and Interfaces,” ACM Mobicom, August 2005.P. Kyasanur and N.H. Vaidya 4.M. Kodialam and T. Nandagopal, “Characterizing the Capacity Region in Multi-Radio Multi-Channel Wireless Mesh Networks,” ACM Mobicom, August 2005.M. Kodialam and T. Nandagopal 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.M. Kodialam and T. Nandagopal 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.W. Wang and X. Liu 7.J. Jun and M.L. Sichitiu, “The Nominal Capacity of Wireless Mesh Networks,” IEEE Wireless Communications Magazine, vol. 10, October 2003.J. Jun and M.L. Sichitiu 8.M. Malekesmaeili, M. Shiva, M. Soltan, “Topology Optimization for Backbone Wireless Mesh Networks,” Fifth Annual Conference on Communication Networks and Services Research, 2007.M. Malekesmaeili, M. Shiva, M. SoltanCommunication Networks and Services Research, 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.X. Wu, J. Liu, and G. Chen 10.E. Miorando and F. Granelli, “On Connectivity and Capacity of Wireless Mesh Networks,” IEEE International Conference on Communications, 2007.E. Miorando and F. Granelli 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.J. Huang, L. Wang, and C. Chang 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.J. Huang, L. Wang and C. Chang 13.G. Mergen and L. Tong, “Stability and Capacity of Regular Wireless Networks,” IEEE Transactions on Information Theory, June 2005.G. Mergen and L. Tong