1. 1 Measuring and Modeling the Impact of Wireless Interference Lili Qiu UT Austin Rice University Nov. 21, 2005

2. 2 Introduction Wireless interference affects network capacity 1 Mbps Throughput = 2 Mbps Throughput = 1 Mbps A B D C 1 Mbps A B D C

3. 3 Capacity of Wireless Networks Many research on computing capacity of multi-hop wireless networks Most of it focuses on asymptotic performance bounds –Gupta and Kumar 2000: O(1/sqrt(N)) under optimal node placement O(1/sqrt(NlogN)) under random node placement

4. 4 Community Networking Scenario Asymptotic analysis is not useful in this case 4 houses talk to the central ITAP. What is the maximum possible throughput?

5. 5 Capacity of Wireless Networks A framework to compute network capacity of specific topologies with specific traffic patterns –Our Mobicom 03 paper, joint work with Jain, Padhye, and Padmanabhan

6. 6 Assumptions Fluid model of data transmission Data transmissions can be finely scheduled by an omniscient central entity –The derived network capacity is under optimal scheduling and optimal routing –Applications Assess the efficiency of the existing network protocols Help network provision (e.g., what-if analysis)

7. 7 Interference Models Protocol model –Transmission is successful if d(i,j)  R(i) and any node k with d(k,j)  R’(k) is not tranmitting –Binary interference model Physical model –Transmission is successful if SNR(i,j)  threshold –Non-binary interference model

8. 8 Overview of Our Framework 1.Model the problem as a standard network flow problem Described as a linear program

9. 9 Step 1: Network Flow Model Create a connectivity graph –Each vertex represents a wireless node –Draw a directed edge from vertex A to vertex B if B is within range of A Write a linear program that solves the basic MAXFLOW problem on this connectivity graph Several generalizations possible –Discussed later in the talk.

10. 10 Example: Network Flow Model Linear Program: Maximize Flow out of A Subject to: 1.Flow on any link can not exceed 1 2.At node B, Flow in == Flow out. Answer: 1 (Link 1, Link 2) A B C Connectivity Graph Link capacity = 1 2 1 4 3

11. 11 Overview of Our Framework 1.Model the problem as a standard network flow problem Described as a linear program 2.Represent interference among wireless links using a conflict graph

12. 12 Step 2: Model Interference using Conflict Graph A conflict graph that shows which wireless links interfere with each other Represent each link in the connectivity graph by a vertex in the conflict graph Draw an edge between two vertices if the wireless links interfere with each other Several generalizations possible –Discussed later in the talk.

13. 13 Example: Conflict Graph Connectivity Graph A B C 1 4 2 3 1 2 3 4 Conflict Graph

14. 14 Overview of Our Framework 1.Model the problem as a standard network flow problem Described as a linear program 2.Represent interference among wireless links using a conflict graph 3.Derive constraints on utilization of wireless links using cliques in the conflict graph Augment the linear program to obtain upper bound on optimal throughput

15. 15 Step 3: Clique Constraints At most one of the vertices in a clique can be active at any given instant –Total utilization of links belonging to a clique is  100% MAXFLOW LP can be augmented with these clique constraints to get a better upper bound Speed-up convergence: consider maximal cliques in the conflict graph –A maximal clique is a clique to which we can not add any more vertices

16. 16 Example: Clique Constraints Link capacity = 1 Linear Program: Maximize Flow out of A Subject to: 1.Flow on any link can not exceed 1 * link utilization 2.At node B, Flow in == Flow out. 3.Sum of utilizations of links 1, 2, 3 and 4 (a clique) can not exceed 100% 1 2 34 Clique = {1, 2, 3, 4} A B C 1 4 2 3 Answer = 0.5 (Link1, Link 2)

17. 17 Properties of Clique Constraints Finding all cliques can take exponential time –Moreover, finding all cliques does not guarantee optimal solution (due to odd holes and odd anti- holes) The upper bound is monotonically non- increasing as we find and add new cliques –As we add each clique, the link utilizations are constrained further More computing time can provide better solution

18. 18 Overview of Our Framework 1.Model the problem as a standard network flow problem Described as a linear program 2.Represent interference among wireless links using a conflict graph 3.Derive constraints on utilization of wireless links using cliques in the conflict graph Augment the linear program to obtain upper bound on optimal throughput 4.Derive constraints on utilization of wireless links using independent sets in the conflict graph Augment the linear program to obtain lower bound on optimal throughput

19. 19 Step 4: Independent Set Constraints All links belonging to an independent set can be active at the same time No two independent sets are active at the same time MAXFLOW LP can be augmented with constraints derived from independent sets to get a lower bound Speed up convergence: consider maximal independent sets in the conflict graph –An independent set to which we cannot add any nodes

20. 20 Example: Independent Set Constraints Link capacity = 1 Linear Program: Maximize Flow out of A Subject to: 1.Flow on any link can not exceed 1 * link utilization 2.At node B, Flow in == Flow out. 3.Sum of utilizations of all independent sets can not exceed 100% 4.Utilization of a link can not exceed the sum of utilization of independent sets it belongs to. 1 2 34 Independent sets: {1}, {2}, {3}, {4} A B C 1 4 2 3 Answer = 0.5 (Link1, Link 2)

21. 21 Properties of Independent Set Constraints Lower bound is always feasible –LP also outputs a transmission schedule Finding all independent sets can take exponential time –If we do find all independent sets, the resulting lower bound is guaranteed to be optimal Lower bound is monotonically non-decreasing as we find and add more independent sets –More computing time provides better answers If upper and lower bounds converge, optimality is guaranteed

22. 22 Putting It All Together 1.Model the problem as a standard network flow problem Described as a linear program 2.Represent interference among wireless links using a conflict graph 3.Derive constraints on utilization of wireless links using cliques in the conflict graph Augment the linear program to obtain upper bound on optimal throughput 4.Derive constraints on utilization of wireless links using independent sets in the conflict graph Augment the linear program to obtain lower bound on optimal throughput Iterate over steps 3 and 4 to find progressively tighten bounds on optimal throughput

23. 23 Putting It All Together (Cont.) Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

24. 24 What-if Analysis ScenarioAggregate Throughput Baseline0.5 Double range0.5 Two ITAPs1 Two Radios1 Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

25. 25 Physical Interference Represent wireless links as vertices in conflict graphs Directed conflict graph Weight on edge X->Y represents the fraction of the maximum permissible noise at the receiver of link Y when link X is active Schedulable sets instead of independent sets Non-schedulable sets instead of cliques

26. 26 Other Generalizations Multiple senders and/or receivers –Write LP to solve multi-commodity flow problem Non-greedy sender –Create a virtual sender –Include a “virtual link” of limited capacity from the virtual sender to the real sender in the connectivity graph –This link does not conflict with any other links –LP maximizes flow out of virtual sender Single path routing –Integer linear programming Multiple radios on orthogonal channels –Represent with multiple, non-interfering links between nodes Directional antennas –Include appropriate links in the connectivity graph –Conflict graph can accommodate any interference pattern

27. 27 Other Generalizations (Cont.) Multirate radios Create multiple virtual links corresponding to a physical link, one for each data rate Only one of the virtual links corresponding to a physical link can be active at a time The edge weights (under physical interference model) reflect the specific noise tolerance for each rate Other objectives Any linear function (e.g., fairness or revenue) can be used

28. 28 Limitations Linear programs can take a long time to solve –Especially when single path routing is used There is no guarantee that optimal solution will be found in less than exponential time Upper bound might not converge to optimal even if we find all cliques –Graphs with odd-holes and anti-holes

29. 29 Summary A flexible framework for deriving capacity of specific topologies with specific traffic patterns –Computes upper and lower bounds on optimal throughput –Accommodate various models of network connectivity and interference, routing constraints, traffic demands How to get a conflict graph for a given network? –IMC 05 paper, joint work with Padhye, Agarwal, Padmanabhan, Rao, and Zill

30. 30 Estimate Wireless Interference What is the metric to quantify wireless interference? –Interference is not a binary relationship How to estimate wireless interference? –Using heuristics –Using empirical measurement

31. 31 Pairwise Interference Metric Two links, A->B and C->D –Throughputs U1 and U2 when operating individually U1’ U2’ –Throughputs U1’ and U2’ when operating simultaneously U1 / U2 /Link Interference Ratio (LIR) = (U1 / +U2 / ) / (U1 + U2) –LIR = 1 implies no interference –LIR < 1 implies interference –Not just binary: full range of values between 0 and 1. Challenge: Estimate LIR for all link pairs without requiring O(n 4 ) experiments

32. 32 Existing Heuristics Heuristic 1 –All links in the multi-hop network interfere with each other –Pessimistic Model Heuristic 2 –Links which share an endpoint interfere with each other –Optimistic Model Heuristic 3 –Links AB and CD interfere if

33. 33 Evaluation of Heuristics Experimental Setup –A testbed of 22 nodes, 802.11 wireless cards, RTS/CTS disabled, 75 random links selected, 1000 byte UDP packets for 30 seconds

34. 34 Proves 1 st heuristic wrong Proves 2 nd heuristic wrong Median LIR of 75 links Experimental results showed 3 rd to be pessimistic model Existing heuristics are inaccurate. We need to look for methods to empirically measure wireless interference.

35. 35 Impact of Interference on Unicast Transmissions: #1 Carrier sense –A and C can hear each other. –Only one transmits at a time. AB CD

36. 36 Impact of Interference on Unicast Transmissions: #2 Collision of data packets –Transmissions from A and C collide at B –Reception of data fails at B AB CD

37. 37 Impact of Interference on Unicast Transmissions: #3 Collision of data and ACK packets –ACK from D collides with data from A –Reception of data fails at B AB CD

38. 38 Impact of Interference on Unicast Transmissions: Other Cases 4. Data/ACK collision prevents reception of ACK 5. ACK/ACK collision

39. 39 Impact of Interference on Unicast Transmissions 1.Carrier sense 2.Data/Data collision 3.Data/ACK collision prevents reception of data 4.Data/ACK collision prevents reception of ACK 5.ACK/ACK collision

40. 40 Key Idea Only consider carrier sense (#1) and data packet collisions (#2) –Ignore ACKs Broadcast packets are sufficient for measurements –Consider only sender pairs, instead of link pairs –O(n 2 ) experiments instead of O(n 4 )

41. 41 Methodology Measure A’s receive rate @ B = M Measure C’s receive rate @ D = N Measure A’s receive rate @ B = M // Measure C’s receive rate @ D = N // Broadcast Interference Ratio (BIR) = (B1 / + B2 / ) / (B1 + B2) = 1 no interference < 1 interference Pairwise Interference Individual Broadcasts Hypothesis: BIR is a good approximation of LIR BIR for all pairs can be calculated with O(n 2 ) experiments BIR Captures 1.Carrier sense 2.Data/Data collisions BIR Ignores 1.Data/ACK collisions 2.ACK/ACK collsions 3.AutoRate

42. 42 Evaluation: Baseline Scenario Median LIR and BIR of 75 pairs CDF of |LIR-BIR| 802.11a, full power, 6Mbps, no RTS/CTS. 75 link pairs selected at random. Average of 5 runs Median error is zero!

43. 43 Evaluation: Other Scenarios Three other scenarios 5 days apart

44. 44 Summary of results BIR is a good approximation for LIR in various scenarios –Low power –802.11 a/b/g –Autorate BIR experiments need to be repeated regularly as link interference patterns change over time.

45. 45 Future work More evaluation: –On different testbeds –Different power levels Interference among larger groups of links (not just pairs) Further reduce measurement overhead –Combine heuristics with measurements –Leverage passive measurement

46. 46 Thank you!