1. 1 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. On the Capacity of Wireless CSMA/CA Multihop Networks Rafael Laufer and Leonard Kleinrock Bell Labs, UCLA IEEE INFOCOM 2013

2. 2 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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 INTRODUCTION Wireless CSMA/CA Multihop Networks U2(t)U2(t) t 213 1 1

3. 3 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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 INTRODUCTION Wireless CSMA/CA Multihop Networks

4. 4 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Understand throughput limits of wireless CSMA/CA multihop networks Provide answers to specific questions regarding the network capacity ­If the rate of f 1 increases by 10%, how much can f 2 still achieve? ­If f 3 starts, by how much must f 1 and f 2 slow down to keep the network stable? Determine the capacity region of arbitrary wireless networks INTRODUCTION Goals f2f2 f1f1 f3f3

5. 5 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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 INTRODUCTION Key Contributions

6. 6 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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 MODEL AND ASSUMPTIONS System Model

7. 7 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. THROUGHPUT MODELING

8. 8 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SATURATED SINGLE-HOP FLOWS All Nodes Within Carrier Sense Range

9. 9 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SATURATED SINGLE-HOP FLOWS All Nodes Within Carrier Sense Range U1(t)U1(t) t 1 U2(t)U2(t) t U3(t)U3(t) t

10. 10 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. By definition, the steady-state solution is Ratio between and SATURATED SINGLE-HOP FLOWS All Nodes Within Carrier Sense Range

11. 11 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. System of linear equations Steady-state solution Throughput of each flow SATURATED SINGLE-HOP FLOWS All Nodes Within Carrier Sense Range

12. 12 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SATURATED SINGLE-HOP FLOWS Not All Nodes Within Carrier Sense Range 2 1 3

13. 13 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SATURATED SINGLE-HOP FLOWS Not All Nodes Within Carrier Sense Range U1(t)U1(t) t U2(t)U2(t) t U3(t)U3(t) t

14. 14 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Steady-state solution for this case General solution Throughput of each flow SATURATED SINGLE-HOP FLOWS Not All Nodes Within Carrier Sense Range

15. 15 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. UNSATURATED SINGLE-HOP FLOWS Idle Time U1(t)U1(t) t 1 U2(t)U2(t) t U3(t)U3(t) t

16. 16 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Steady-state solution Source behavior ­Injecting too little traffic: 0 ­Injecting too much traffic: 1 UNSATURATED SINGLE-HOP FLOWS

17. 17 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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/ UNSATURATED SINGLE-HOP FLOWS

18. 18 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. UNSATURATED SINGLE-HOP FLOWS Primal Unsaturated Network U1(t)U1(t) t 1 U2(t)U2(t) t U3(t)U3(t) t

19. 19 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. UNSATURATED SINGLE-HOP FLOWS Dual Saturated Network U1(t)U1(t) t U2(t)U2(t) t U3(t)U3(t) t 1

20. 20 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION CHARACTERIZATION

21. 21 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Normalized throughput of transmitter i Express as a function of Find the inverse Limit the stability factors to the range CAPACITY REGION Characterization Algorithm

22. 22 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Two Transmitters Within Carrier Sense Range

23. 23 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Two Transmitters Within Carrier Sense Range 1 y1y1 y2y2 1

24. 24 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Three Transmitters Within Carrier Sense Range

25. 25 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Three Transmitters Within Carrier Sense Range 1 y1y1 y2y2 1 y3y3 1

26. 26 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Three Transmitters Not Within Carrier Sense Range 2 1 3

27. 27 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Three Transmitters Not Within Carrier Sense Range 1 y1y1 y2y2 1 Capacity lost due to the lack of synchronization between nodes

28. 28 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. CAPACITY REGION Three Transmitters Not Within Carrier Sense Range 1 y1y1 y2y2 1 y3y3 1

29. 29 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. FEASIBILITY TEST

30. 30 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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 FEASIBILITY TEST Feasibility of Input Rates

31. 31 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SIMULATION RESULTS

32. 32 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SIMULATION SCENARIO MIT Roofnet Network: Single-Hop Flows

33. 33 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SIMULATION RESULTS Single-Hop Flows (ρ = 1.00)

34. 34 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SIMULATION RESULTS Single-Hop Flows (ρ = 0.50)

35. 35 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SIMULATION RESULTS Single-Hop Flows (ρ = 0.25)

36. 36 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. SIMULATION RESULTS Single-Hop Flows (ρ = 0.01)

37. 37 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 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 CONCLUSIONS

38. 38 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. On the Capacity of Wireless CSMA/CA Multihop Networks Rafael Laufer and Leonard Kleinrock Bell Labs, UCLA IEEE INFOCOM 2013