FraNtiC : A Fractal Geometric Framework for Mesh-Based Wireless Access Networks

1. University of Texas at Arlington FraNtiC : A Fractal Geometric Framework for Mesh-Based Wireless Access Networks Samik Ghosh, Kalyan Basu and Sajal Das Center For Research In Wireless Mobility & Networking (CReWMaN)

2. OutLine • The Next Generation “Network Utopia” • Technological Challenges • The Case for Wireless Mesh • The FraNtiC Framework • Flexibility & Scalability • Robustness • Network Exposure • Reliability • Performance of the FraNtiC Framework • Conclusion • References

3. The Next Generation Wireless Dream • “Network Utopia” – a “world of smart intercommunicating everything” • Current and Emerging Wireless Technologies IMT-2000/3GPP,MBS, BWA • Broadband Data-centric Services – digital multimedia broadcasting, mobile gaming • Seamless co-existence of heterogeneous wireless technologies • IEEE Spectrum (North American Edition), Vol.41, No.11, Nov. 2004, pp.14.

4. Next generation network architecture

5. Technological Challenges • Increased data-rates and backhaul traffic • High Capacity and low cost per bit • Scalable, flexible and easily configurable network topology • Carrier-class network reliability • Low-cost, high-bandwidth backhaul transmission • Low overhead control messages and low handover latency

6. Current Access Network Perspective • The Network is primarily designed to support circuit-switched traffic • The current network infrastructure is untenable for high-capacity, high-data rate micro-cellular services • Current Backhaul use TDM based T1/E1 links which incur huge costs

7. The Case for Wireless Mesh • High level of coverage • Low cost of deployment and maintenance • Multiple redundant paths to ensure reliability • Flexibility in configuration • Scalability with changing network dynamics

8. Gen-1 Gen- 0 Gen-2 The FraNtiC Framework - Fractal Structure • A deterministic way of generating a self-similar geometry – a variant of the Sierpinski Gasket, Pascal –Sierpinski Fractal • No. of self-similar pieces at the gth generation = 22g • Magnification Factor at the gth generation = 2g • Fractal Dimension =2 Generator Initiator

9. 2 1 1 2 The FraNtiC Framework • A mesh-based access network is formed by connecting each base-stations to its neighbors only • The mesh-based access network can be mapped to the fractal structures at various generations of evolution

10. Salient Features • Number Of nodes and edges at the gth generation RNS 2 Where lg = no. of levels = 2g • Number Of nodes at each level is i , where i = 1,2….k • Node Density in successive generations • Topological features are invariant to scale

11. Flexibility & Scalability - The self-repetitive and scale-invariance properties make the architecture highly scalable - As the number of cells increase, the framework essentially evolves to higher generations to support the increased cells

12. Topological Robustness - Ability of the network to tolerate perturbations resulting from loss of edges and/or nodes - Measured in terms of “size of largest component” due to edge/node loss under error or attack scenarios Size of largest component Vs fraction of node and link failure

13. Centrality and Its Role in RNC Selection - “Centrality” has been used in social networks to study the power yielded by various nodes in a network - “Closeness Centrality” measures the geodesic distance of a node to all other nodes in the network - “Betweenness Centrality” of a node is defined as the number of geodesics passing through the node where is the closeness centrality of node v, E is the edge-set and is the shortest distance between nodes v and w

14. Choice of Network Controller Location • High value of Centrality index will minimize delay and reduce routing cost • High value can increase network vulnerability • Centrality Characteristics of FraNtiC Decentralization

15. “Exposed” Network Exposure • Network Exposure () – total traffic “exposed” due to perturbations caused by node/link failures • Depends on network topology, traffic patterns and the set of failed links/nodes

16. Network Exposure Computation (a) General Algorithm NXCalc (g) /*Traffic matrix, distance matrix and adjacency matrix are computed*/ /* g is the generation whose network exposure is being computed */ compute Ng, Eg for(f=1 to Eg ) for (j=1 to all combinations of f link failures of Eg links) generate new adjacency matrix with f edges deleted according to the jth configuration Pj = calculate proabability of the jth configuration Ej =calculate the traffic exposed due to this configuration avgExposure = avgExposure + Pj*Ej EndFor EndFor EndAlgo. (b) Recursive Algorithm NXCalcR ( g, gBase) /* g is the generation whose network exposure is being computed */ /* gBase is the base generation */ if ( g equals gBase) minXposure = // calculate exposure using brute force method else minXposure = mink(NXCalcR ( g-1, gBase)), where k is the number of g ¡ 1 generation fractal structures.

17. Reliability and Resiliency Issues • The fractal generator structure is considered as the base and reliability of a nth generation RNS is calculated recursively on the basis of the base case • Considering rs = link availability at stage s

18. where Rt is the reliability of a node of type t ( i.e the probability that node t can communicate with its serving RNC node is given as, • The reliability of the RNS

19. The more general case of reliability of the nth generation RNS can be expressed as Reliability of a A-node RNC of the n-1th generation and,

20. Performance of FraNtiC Framework • The links are modeled using Optical Wireless system parameters and link availability is calculated accordingly

21. Low link availability Link Reliability Vs Cell Side Exposure decrease with generation Avg. Network Exposure Vs. No. of link failures

22. Performance Comparison Algorithm Step 1 : Initialization (a) Initialize RNC Switching Capacity and RNC port constraints (b) Initialize no. of nodeBs (N) (c) Generate the distance matrix and traffic vectors Step 2: Generate the complete graph on N nodes Step 3: Find the MST ( based on link distances as edge weights) Step 4: Partition the tree into clusters based on RNC Switching and Port Constraints[kundu] Step 5: For each cluster generated reconnect the cluster nodes in a corresponding tree, FraNtiC and square grid topology. Calculate All-terminal network reliability on the topology Calculate system cost based on cost models for each topology Calculate average network exposure EndFor Step 6 : Calculate Normalized exposure, total system cost and min. network reliability for each topology

23. Performance Comparison on a sample access network

24. Network Reliability Vs. No. of Nodes

25. System Cost Vs. No. of Nodes

26. Difference in exposure for similar traffic pattern Network Exposure Vs. No. of Nodes

27. Conclusions • A generic fractal framework for mesh based access networks • The framework lends itself to scale and evolve with dynamically changing network behavior • The framework provides flexibility in design on account of its topological properties • Provides carrier-class reliability • Incurs low system deployment costs • Reduces network exposure

28. References • P. Whitehead, “Mesh networks: a new architecture for broadband wireless access systems”. Radio and Wireless Conference, IEEE RAWCON, Page(s): 43 –46, 10-13 Sept. 2000 • A. Acampora and S.V Krishnamurthy, “A Broadband wireless access network based on mesh-connected free-space optical links”, IEE Wireless Communications , Vol.6, No.5, Oct 1999 • Reka Albert, Hawoong Jeong, A. Barabasi, “Error and Attack Tolerence of complex networks” , Nature magazine, Vol.406, July 2000. • Ulrich Lauther, Thomas Winter, Mark Zeigelmann, “ Proximity Graph Based Clustering Algorithms For Optimized planning of UMTS Access Network Topologies”, ICT 2003 • T. Otsu, I. Okajima, N. Umeda, Y. Yamao, “Network architecture for mobile communications systems beyond IMT-2000” , IEEE Personal Communications, Volume: 8 Issue: 5 , Page(s): 31 –37, Oct. 2001 • S. Havlin, A. Bunde, “Fractals and Disordered Systems”, Springer, 1991. • R. Karrer, A. Sabharwal, and E. Knightly, “Enabling Largescale Wireless Broadband: The Case for TAPs”, HotNets 2003. • L. C. Freeman, “Centrality in social networks: conceptual clarification”, Social Networks, 1979. • .P Borgatti, M.G Everett, L.C Freeman, “Ucinet for Windows: Software for Social Network Analysis.”, Harvard, Analytic Technologies. • IEEE Spectrum (North American Edition), Vol.41, No.11, Nov. 2004, pp.14.