Measuring and Modeling the Impact of Wireless Interference

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

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

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

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

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

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

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

14. Overview of Our Framework • Model the problem as a standard network flow problem • Described as a linear program • Represent interference among wireless links using a conflict graph • 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. 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. 2 1 3 4 Example: Clique Constraints 2 1 C B A 3 4 Link capacity = 1 Clique = {1, 2, 3, 4} • Linear Program: • Maximize Flow out of A • Subject to: • Flow on any link can not exceed 1 * link utilization • At node B, Flow in == Flow out. • Sum of utilizations of links 1, 2, 3 and 4 (a clique) can not exceed 100% Answer = 0.5 (Link1, Link 2)

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. Overview of Our Framework • Model the problem as a standard network flow problem • Described as a linear program • Represent interference among wireless links using a conflict graph • Derive constraints on utilization of wireless links using cliques in the conflict graph • Augment the linear program to obtain upper bound on optimal throughput • 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. 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. Example: Independent Set Constraints 2 1 2 1 C B A 3 4 3 4 Independent sets: {1}, {2}, {3}, {4} Link capacity = 1 • Linear Program: • Maximize Flow out of A • Subject to: • Flow on any link can not exceed 1 * link utilization • At node B, Flow in == Flow out. • Sum of utilizations of all independent sets can not exceed 100% • Utilization of a link can not exceed the sum of utilization of independent sets it belongs to. Answer = 0.5 (Link1, Link 2)

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. Putting It All Together • Model the problem as a standard network flow problem • Described as a linear program • Represent interference among wireless links using a conflict graph • Derive constraints on utilization of wireless links using cliques in the conflict graph • Augment the linear program to obtain upper bound on optimal throughput • 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. Putting It All Together (Cont.) Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

24. What-if Analysis Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

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. 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. 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. 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. 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. 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. Pairwise Interference Metric • Two links, A->B and C->D • Throughputs U1 and U2when operating individually • Throughputs U1’and U2’ when operating simultaneously • 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(n4) experiments

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. 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. Proves 1stheuristic wrong Proves 2nd heuristic wrong Median LIR of 75 links Experimental results showed3rd to be pessimistic model Existing heuristics are inaccurate. We need to look for methods to empirically measure wireless interference.

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

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 A B C D

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 A B D C

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

39. Impact of Interference on Unicast Transmissions • Carrier sense • Data/Data collision • Data/ACK collision prevents reception of data • Data/ACK collision prevents reception of ACK • ACK/ACK collision

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(n2) experiments instead of O(n4)

41. Methodology Individual Broadcasts Pairwise Interference Measure A’s receive rate @ B = M Broadcast Interference Ratio (BIR) = (B1/+ B2/) / (B1 + B2) Measure A’s receive rate @ B = M// • = 1 no interference • < 1 interference BIR for all pairs can be calculated with O(n2) experiments Hypothesis: BIR is a good approximation of LIR • BIR Captures • Carrier sense • Data/Data collisions • BIR Ignores • Data/ACK collisions • ACK/ACK collsions • AutoRate Measure C’s receive rate @ D =N Measure C’s receive rate @ D = N//

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

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

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. 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. Thank you!