1. Capacity of wireless ad-hoc networks By Kumar Manvendra October 31,2002

2. Outline Problem definition What is meant by the capacity ? Why is it relevant ? What are the issues involved ? Example scenarios with various simulation environments Performance results Open problems Summary Future Work References

3. Problem Definition Capacity of Ad-Hoc Wireless Networks A measure of the amount of data that can be transmitted simultaneously in an ad-hoc wireless network Alternative explanation: Lack of congestion losses and misrouting of packets Problems Overall capacity decreases with increase in non-local traffic and number of nodes because they have to forward each others packets Spatial reuse doesnt seem to help that much

4. Factors influencing Capacity Traffic Pattern Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-hoc network

5. Need to explain the issues involved Gupta and Kumar[3] showed that for static nodes, as number of nodes per unit area,n, increase …the throughput per source-destination pair decreases like 1/SQRT(N)

6. Example #1 : Capacity of a chain of nodes 1 MAC interference among a chain of nodes 234 6 Radio Range of Node Interference Range of Node 4 5 Inter-nodal distance = 200 ms

7. Example #1 : Capacity of a chain of nodes MAC interference among a chain of nodes 1234 6 Radio Range of Node (200 ms) Interference Range of Node 4 5

8. Example #1 : Capacity of a chain of nodes 1 MAC interference among a chain of nodes 23 4 6 Radio Range of Node(200 ms) Interference Range of Node 4(550 ms) 5

9. Example #1 : Capacity of a chain of nodes 1 MAC interference among a chain of nodes 23 4 6 Radio Range of Node 5 Radio Range of Node(200 ms) Interference Range of Node 4(550 ms)

10. Example #1 : Capacity of a chain of nodes 1 MAC interference among a chain of nodes 23 4 6 Radio Range of Node 5 Assuming radios of non-neighboring nodes do not interfere with each other Radio Range of Node(200 ms) Interference Range of Node 4(550 ms)

11. Example #1 : Capacity of a chain of nodes 1 MAC interference among a chain of nodes 23 4 6 Radio Range of Node Interference Range of Node 4 5 Assuming radios of non-neighboring nodes do not interfere with each other Total Max. Channel Utilization = 1/3

12. Example #1 : Capacity of a chain of nodes 1 MAC interference among a chain of nodes 23 4 6 Radio Range of Node Interference Range of Node 4 5 Assuming interference range interfere with non-neighboring nodes Total Max. Channel Utilization = 1/4

13. Simulation Performance Results – single chain of nodes 64 B 500 B 1500 B With Longer Chains, Utilization levels go substantially low. For a 1500 Byte packet size, it is as low as 15%

14. Simulation Performance Results – single chain of nodes 64 B 500 B 1500 B With Longer Chains, Utilization levels go substantially low. For a 1500 Byte packet size, it is as low as 15% Mimics results from actual hardware testing also 1)802.11 is incapable of discovering an optimal schedule of transmissions 2)Inherent unfairness because nodes at the end send in more packets than nodes in the middle can forward 3)Back-offs cause wastage

15. Analysis of Performance Results With increase in the length, per node Interference increases. So, per node waste of bandwidth increases. For example, in the example above, Node #1s send rate is 0.48 while nodes further along the link can only forward at the rate of 0.26-0.35 23 6 Radio Range of Node Interference Range of Node 4 1 4

16. Analysis of Performance Results Waste in terms of back-off Periods For Example : Node #1 wasted back-off time is 5.4% of total time 1234 6 Radio Range of Node Interference Range of Node 5

17. Two communication patterns Example #2 : Capacity of a regular lattice network Scenario #1 Scenario #2

18. Scenario #1 Example #2 : Capacity of a regular lattice network Internode Distance = 200 ms Interference radius = 550 ms Every third row can operate Without interference to give a Maximum throughput of 1/4 Thus flow in such a lattice network is expected (theoretically) to reach 1/12

19. Performance Results for Lattice simulations 60 B 500 B 1500 B Same inefficiencies as in chain list : Disproportionate traffic per node And wasted back - off time( close to 0.75%)

20. Scenario #2 Example #2 : Capacity of a regular lattice network Traffic flow direction 1) Optimal Scheduling possible with predetermined routes. 2) Overall throughput can be maximized (in theory) with one vertical flow in one time unit and horizontal flows in another

21. Performance Analysis 1500 B500 B 60 B Possible Problem : Since each node has a single queue per flow, if a packet to be sent horizontally is waiting for contention, the packet to be sent vertically might lose its chance to be sent Wasted time due to Back-off as high as 2.25%

22. Example Scenario #3 : Random traffic random layout Assuming total randomness of nodes placement and destination selection for each sending node. Assuming pre-computed paths

23. Performance Results – comparison with lattices 1500 Bytes packets horizontal Horizontal and vertical random Random networks have somewhat less capacity than lattices because more packets routed through the center of the network, and not enough spatial reuse

24. Another Perspective : Load imposed due to networks nodes One-hop capacity depends upon the amount of spatial reuse possible in the network and depends upon Number of nodes Inter-nodal distance Physical area covered in the network Mathematical analysis : For packet rate,R,….communication radius, r And expected physical path length L One Hop Capacity of the network to send and forward packets C > n. R. (L/r) Assuming uniform node density, D, and number of nodes,n …Capacity, C is also equal to k(n/D), where k is a constant. Therefore, per node capacity, R(packet rate), is R < k(r/D)*(1/L) = (C/n) / (L/r)

25. Factors influencing Capacity Traffic Pattern Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-hoc network

26. Factors influencing Capacity Traffic Pattern Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-hoc network

27. Factors influencing Capacity Traffic Pattern Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-hoc network

28. Another Perspective : Load imposed due to networks nodes One-hop capacity depends upon the amount of spatial reuse possible in the network and depends upon Number of nodes Inter-nodal distance Physical area covered in the network Mathematical analysis : For packet rate,R,….communication radius, r And expected physical path length L One Hop Capacity of the network to send and forward packets C > n. R. (L/r) Assuming uniform node density, D, and number of nodes,n …Capacity, C is also equal to k(n/D), where k is a constant. Therefore, per node capacity, R(packet rate), is R < k(r/D)*(1/L) = (C/n) / (L/r)

29. Recap Per Node Capacity = (Average One hope Capacity) / (Expected Path Length) R = (C/n) / (L/r) or Inference : As expected path length increases, the bandwidth available to each node decreases. Inference: Since capacity is determined by traffic patterns, the most capacity enhancing traffic pattern is strictly local because expected path length remains constant

30. Recap Per Node Capacity = (Average One hope Capacity) / (Expected Path Length) R = (C/n) / (L/r) or Inference : As expected path length increases, the bandwidth available to each node decreases. Inference: Since capacity is determined by traffic patterns, the most capacity enhancing traffic pattern is strictly local because expected path length remains constant

31. Effects of Mobility If a wireless network with many users, authors contend that optimal strategy is to allocate the bandwidth to the user who can best use it. Assumptions of asynchronous applications and high threshold of tolerable delays On the above assumption, per node throughput can be kept constant distributing packets to as many nodes as possible (each with difference time variance) transmitting only when nodes are close together so as to minimize interference And hence, probabilistically, maximizing the overall throughput

32. Summary Capacity in an ad-hoc wireless network depends upon the following : Number of nodes Density Traffic pattern Mobility Communication radius/interference

33. References Capacity of Ad-Hoc wireless networks, Li, Blake, Couto, Lee, Morris Mobility increases the capacity of ad- hoc wireless networks, Grossglauser, Tse The Capacity of Wireless Networks, Gupta and Kumar