On the Capacity of Wireless CSMA/CA Multihop Networks

1. On the Capacity of Wireless CSMA/CA Multihop Networks Rafael Laufer and Leonard KleinrockBell Labs, UCLA IEEE INFOCOM 2013

2. INTRODUCTIONWireless CSMA/CA Multihop Networks • Carrier sense multiple access with collision avoidance (CSMA/CA) • Before transmitting, the node verifies if the medium is idle via carrier sensing • If idle, sample a random back-off interval and starts counting down • Whenever busy, freeze the counter and wait for ongoing transmission to finish 1 2 3 U2(t) 1 1 t

3. INTRODUCTIONWireless CSMA/CA Multihop Networks • Considered unpredictable with unknown throughput limitations • Distributed nature of CSMA/CA: nodes should back off from each other • Buffer dynamics of unsaturated sources: time-varying subset of transmitters • Dependence of downstream links on upstream traffic: coupled queue state • Strong dependence among the state of transmitters • Physical proximity and traffic pattern induce correlation across the network

4. INTRODUCTIONGoals • Understand throughput limits of wireless CSMA/CA multihop networks • Provide answers to specific questions regarding the network capacity • If the rate of f1 increases by 10%, how much can f2 still achieve? • If f3 starts, by how much must f1 and f2 slow down to keep the network stable? • Determine the capacity regionof arbitrary wireless networks f2 f3 f1

5. INTRODUCTIONKey Contributions • Theory to model the behavior of wireless CSMA/CA multihop networks • Handle buffer dynamics of unsaturated traffic sources and multihop flows • Respect interference constraints imposed by the wireless medium • Characterization of the capacity region of any wireless network • No restrictions on node placement: suitable for arbitrary networks • Agnostic to the distribution of network parameters: only averages are relevant • Convex only when nodes are within range: nonconvex in general • Feasibility test

6. MODEL AND ASSUMPTIONSSystem Model • Single-path routing, with routes and bit rates assumed fixed • Omnidirectional antenna communicating in a single channel • CSMA/CA for medium access control • Network state S composed of links transmitting • Knowledge of the feasible link sets in the network • : fraction of time that all links in S are transmitting

7. THROUGHPUT MODELING

8. SATURATED SINGLE-HOP FLOWSAll Nodes Within Carrier Sense Range

9. SATURATED SINGLE-HOP FLOWSAll Nodes Within Carrier Sense Range U1(t) 1 t U2(t) t U3(t) t

10. SATURATED SINGLE-HOP FLOWSAll Nodes Within Carrier Sense Range • By definition, the steady-state solution is • Ratio between and

11. SATURATED SINGLE-HOP FLOWSAll Nodes Within Carrier Sense Range • System of linear equations • Steady-state solution • Throughput of each flow

12. SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense Range 1 3 2

13. SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense Range U1(t) t U2(t) t U3(t) t

14. SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense Range • Steady-state solution for this case • General solution • Throughput of each flow

15. UNSATURATED SINGLE-HOP FLOWSIdle Time U1(t) 1 t U2(t) t U3(t) t

16. UNSATURATED SINGLE-HOP FLOWS • Steady-state solution • Source behavior • Injecting too little traffic:  0 • Injecting too much traffic:  1

17. UNSATURATED SINGLE-HOP FLOWS • Why the solution is similar to the saturated case? • Statistically equivalent to a saturated network • Average transmission times are the same • Average backoff times are larger by 1/

18. UNSATURATED SINGLE-HOP FLOWSPrimal Unsaturated Network U1(t) 1 t U2(t) t U3(t) t

19. UNSATURATED SINGLE-HOP FLOWS Dual Saturated Network U1(t) 1 t U2(t) t U3(t) t

20. CAPACITY REGION CHARACTERIZATION

21. CAPACITY REGIONCharacterization Algorithm • Normalized throughput of transmitter i • Express as a function of • Find the inverse • Limit the stability factors to the range

22. CAPACITY REGIONTwo Transmitters Within Carrier Sense Range

23. CAPACITY REGIONTwo Transmitters Within Carrier Sense Range y1 1 y2 1

24. CAPACITY REGIONThree Transmitters Within Carrier Sense Range

25. CAPACITY REGIONThree Transmitters Within Carrier Sense Range y1 1 y2 1 1 y3

26. CAPACITY REGIONThree Transmitters Not Within Carrier Sense Range 1 3 2

27. CAPACITY REGIONThree Transmitters Not Within Carrier Sense Range y1 1 Capacity lost due to the lack of synchronization between nodes y2 1

28. CAPACITY REGIONThree Transmitters Not Within Carrier Sense Range y1 1 y2 1 1 y3

29. FEASIBILITY TEST

30. FEASIBILITY TESTFeasibility of Input Rates • Does the network support a given rate vector ? • Normalized throughput depends only on average values • approximates the total transmission time as • approximates the total time as • Plug into the expression and check if

31. SIMULATION RESULTS

32. SIMULATION SCENARIOMIT Roofnet Network: Single-Hop Flows

33. SIMULATION RESULTSSingle-Hop Flows (ρ = 1.00)

34. SIMULATION RESULTSSingle-Hop Flows (ρ = 0.50)

35. SIMULATION RESULTSSingle-Hop Flows (ρ = 0.25)

36. SIMULATION RESULTSSingle-Hop Flows (ρ = 0.01)

37. CONCLUSIONS • Capacity of wireless CSMA/CA multihop networks poorly understood • Theory able to model the network behavior • Buffer dynamics of unsaturated sources and multihop flows • Wireless CSMA/CA multihop networks are not erratic, but predictable • System of nonlinear equations characterizes the network capacity • Agnostic to the distribution of network parameters, only averages relevant • Knowledge of the underlying process governing CSMA/CA networks • Opens up new areas of research • Routing optimization and network provisioning

38. On the Capacity of Wireless CSMA/CA Multihop Networks Rafael Laufer and Leonard KleinrockBell Labs, UCLA IEEE INFOCOM 2013