Theoretical Capacity of Multi-hop Wireless Ad Hoc Networks

1. Theoretical Capacity of Multi-hop Wireless Ad Hoc Networks Yue Fang A.Bruce McDonald R-WIN Lab ECE Department Northeastern University MWCN 2004

2. Outline • Introduction • Network Saturation Capacity • Maximum Instantaneous Capacity • Discussion MWCN 2004

3. Outline • Introduction • Network Saturation Capacity • Maximum Instantaneous Capacity • Discussion MWCN 2004

4. Wireless Ad Hoc Networks • Easy to setup, no wiring required • Provides support of mobile (and ubiquitious) computing • Limited resources • Lower capacity • Dynamic characteristics MWCN 2004

5. 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 MWCN 2004

6. 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. MWCN 2004

7. Topology Generation Network topology is generated by repeating specific patterns to avoid unnecessary randomness. navg=3 navg=6 MWCN 2004

8. Outline • Introduction • Network Saturation Capacity • Maximum Instantaneous Capacity • Discussion MWCN 2004

9. 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. MWCN 2004

10. Previous Work (2) D • 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. C E X F A G B X I H Only communication between C and F will affect the communication between A and B, thus the equivalent competitor is 1/3. MWCN 2004

11. Network Saturation Capacity (NSC) • It is necessary to study the relation between the capacity and node location. MWCN 2004

12. 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). MWCN 2004

13. A 2r-d B α d 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. MWCN 2004

14. NSC: How big is big? Number of Phantom Nodes # of phantom nodes/ total nodes • 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. Percentage of phantom nodes to Num Number of phantom nodes vs. R/r MWCN 2004

15. Outline • Introduction • Network Saturation Capacity • Maximum Instantaneous Capacity • Discussion MWCN 2004

16. 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. MWCN 2004

17. 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 Bottleneck is the MIC: c3 c1 simultaneous links c2 simultaneous links c3 simultaneous links c1>= c2>=c3 MWCN 2004

18. 1 (1,2) 2 (3,4) (4.5) 3 5 (2,3) (2,5) 4 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]. MWCN 2004

19. MIC: The greedy Algorithm • List all the feasible deferral sets in ascending order by the number of links in each set. • Pick the first deferral set in the list , transmission along corresponding link can be granted. • If more than one deferral set have same size, the tie is broken by activating the link with minimum LOS (line-of-sight) distance. • Update the candidate deferral list. • Update the size of remaining feasible deferral sets. • Repeat 1-5 until the candidate deferral set list is empty. MWCN 2004

20. n avg Random Link Selection • Randomly select the link to be activated. • Faster than greedy heuristic • Results are of the same order. MWCN 2004

21. 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. MWCN 2004

22. n avg Experimental Result Number of requited iterations and corresponding lower bound MWCN 2004

23. Outline • Introduction • Network Saturation Capacity • Maximum Instantaneous Capacity • Discussion MWCN 2004

24. 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] MWCN 2004

25. 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: MWCN 2004

26. 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. MWCN 2004

27. 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 MWCN 2004