1. 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign

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3. 3 Multi-Channel Wireless Networks: Theory to Practice Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign

4. 4 Wireless Networks  Infrastructure-Based Networks  Infrastructure-Less (and Hybrid) Networks: –Mesh networks, ad hoc networks, sensor networks

5. What Makes Wireless Networks Interesting?  Broadcast channel  Interference management non-trivial  Signal-interference are relative notions A B C D power Signal Interference

6. 6 What Makes Wireless Networks Interesting? Many forms of diversity Time Route Antenna Path Channel

7. 7 What Makes Wireless Networks Interesting? Antenna diversity C D A B Sidelobes not shown

8. 8 What Makes Wireless Networks Interesting? Path diversity x 1 x 2 y 1 y 2

9. 9 What Makes Wireless Networks Interesting? Channel diversity A B A B Low gain High gain A B C D A B C D Low interference High interference

10. Research Challenge Dynamic adaptation to exploit available diversity 10

11. 11 Net-X Multi- Channel Wireless Mesh Theory to Practice Multi-channel protocol Channel Abstraction Module IP Stack Interface Device Driver User Applications ARP Interface Device Driver OS improvements Software architecture Capacity & Scheduling channels capacity A B C D E F Fixed Switchable Insights on protocol design Net-X testbed

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13. Secret to happiness is to lower your expectations to the point where they're already met 13 with apologies to Bill Watterson (Calvin & Hobbes)

14. 14 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign

15. Distributed Algorithms & Communications 15 Communications / Networking Distributed Algorithms

16. Distributed Algorithms & Communications  Problems with overlapping scope  But cultures differ 16 Communications / Networking Distributed Algorithms

17. 17 Distributed Algorithms Black box networks Emphasis on order complexity Emphasis on “exact” performance metrics Constants matter Communications / Networking

18. 18 Distributed Algorithms Black box networks Emphasis on order complexity Emphasis on “exact” performance metrics Constants matter Information transfer (typically “raw” info) Communications / Networking

19. 19 Distributed Algorithms Computation affects communication Emphasis on “exact” performance metrics Constants matter Information transfer (typically “raw” info) Communications / Networking Black box networks Emphasis on order complexity

20. Distributed Algorithms & Communications 20 Communications / Networking Distributed Algorithms

21. Outline Two distributed algorithms  Byzantine agreement  Scheduling (CSMA) 21 Rate Region Communications / Networking Distributed Algorithms

22. Rate Region  Defines the way links may share channel  Interference posed to each other determines whether a set of links should be active together 22

23. “Ethernet” Rate Region 23 S 1 2 Rate S1 + Rate S2 ≤ C R1 + R2 ≤ C Private channels S1 and S2 Rate S1 Rate S2 sum-rate constraint

24. Point-to-Point Network Rate Region Rij ≤ Capacity ij 24 S 1 2 Each directed link independent of other links

25. Wireless Network: Rate Region  Some links share channel with each other while others don’t 12 4 3 R1 R2 R3 max(R1/C1, R3/C3) + (R2/C2) ≤ 1

26. Broadcast Channel: Rate Region R ≤ C1 S 2 3 1

27. Broadcast Channel: Rate Region > C1 S 2 3 R ≤ C2 “Range” varies inversely with rate 1

28. Broadcast Channel S 2 3 1 S 2 3 1 R1 R2 R12 R1/C1 + R2/C2 + R12/C12 ≤ 1

29. Outline Two distributed algorithms  Byzantine agreement  Scheduling (CSMA) 29

30. Impact of Rate Region  Network rate region affects ability to perform multi-party computation  Example: Byzantine agreement (broadcast) 30

31. Byzantine Agreement: Broadcast Source S wants to send message to n-1 receivers  Fault-free receivers agree  S fault-free  agree on its message  Up to f failures

32. Impact of Rate Region  How does rate region affect broadcast performance ?  How to quantify the impact ? 32

33. Throughput of Agreement  Borrow notion of throughput from communications literature  b(t) = number of bits agreed upon in [0,t] 33 Long timescale measure

34. Capacity of Agreement  Supremum of achievable throughputs for a given rate region

35. Broadcast Channel Rate region R ≤ C 35 Agreement capacity = C S 2 3 1 R

36. “Ethernet” Rate Region  Sum of private link capacities ≤ C 36 Agreement capacity = C Communication complexity per agreed bit 1 S 2 3

37. “Ethernet” Rate Region Communication complexity per-agreed bit 37 L number of bits required to agree on L bits =

38. “Ethernet” Rate Region Communication complexity per-agreed bit 38 L number of bits required to agree on L bits =

39. “Ethernet” Rate Region Communication complexity per-agreed bit  L = 1 : Ω(n 2 ) for n node [Dolev-Reischuk] (deterministic algorithms) 39 L number of bits required to agree on L bits =

40. “Ethernet” Rate Region Communication complexity per-agreed bit  L = 1 : Ω(n 2 ) for n nodes  L  ∞ : can be shown O(n) (multi-value agreement) 40 L number of bits required to agree on L bits =

41. “Ethernet” Rate Region Communication complexity per-agreed bit  L = 1 : Ω(n 2 ) for n nodes  L  ∞ : can be shown O(n) (multi-value agreement) 41 L number of bits required to agree on L bits = 41 bits per agreed-bit n(n-1) (n-f)

42. “Ethernet” Rate Region  Sum of private link capacities ≤ C 42 Agreement capacity ≥ C n(n-1) (n-f) Conjecture: tight bound 1 S 2 3

43. A S B C Point-to-Point Network Each link has its own capacity Load ij ≤ Cij

44. A S B C 4 2 4 3 3 4 4 3 3 Point-to-Point Network Each link has its own capacity Cij as shown Agreement Capacity ?

45. Point-to-Point Network Cij as shown Agreement Capacity = 2 A S B C 4 2 4 3 3 4 4 3 3

46. Point-to-Point Network є Cij as shown Agreement Capacity = 6 A S B C 4 2 4 3 3 4 4 3 3

47. A S B C Point-to-Point Network Capacity-achieving scheme for Arbitrary 4 node networks Approach:  Upper bound based on min-cuts  Lower bound using coding

48. A S B C Point-to-Point Network Capacity-achieving scheme for Arbitrary 4 node networks Minimum number of rounds required depends on link capacities

49. A S B C Point-to-Point Network Open problem: Everything else Capacity-achieving scheme for Arbitrary 4 node networks

50. Open Problems  Capacity-achieving agreement with general rate regions  Subset of nodes as “receivers” 50

51. Open Problems  Capacity-achieving agreement with general rate regions  Subset of nodes as “receivers”  Even the multicast problem with Byzantine nodes is unsolved - For multicast, source S fault-free 51

52. Rich Problem Space  Broadcast channel allows overhearing  Transmit to 2 at high rate, or low rate ? - Low rate allows reception at 1 (broadcast advantage) 52 S 2 3 1

53. Rich Problem Space  Broadcast channel allows overhearing  Transmit to 2 at high rate, or low rate ? - Low rate allows reception at 1 (broadcast advantage) 53 S 2 3 1 Low rate

54. Rich Problem Space  Broadcast channel allows overhearing  Transmit to 2 at high rate, or low rate ? - Low rate allows reception at 1 (broadcast advantage) 54 S 2 3 1 High rate

55. Rich Problem Space  How to model & exploit reception with probability < 1 ? –Need opportunistic algorithms  Use of available diversity affects rate region –How to dynamically adapt to channel variations ? 55

56. Rich Problem Space  Similar questions relevant for any multi-party computation 56 Communications / Networking Distributed Algorithms

57. And Now for Something Completely Different * * Monty Python 57

58. Outline Two distributed algorithms  Byzantine agreement  Scheduling (CSMA) 58

59. Scheduling Objective  Network stability 12 4 3 L0 L2 L3

60. Scheduling Objective  Network stability 12 4 3 L0 L2 L3 12 4 3 L0 L2 L3

61. Scheduling 12 4 3 L0 L2 L3 1/2 Arrival rates

62. 12 4 3 L0 L2 L3 Arrivals in even slots Arrivals in odd slots

63. End of slot 0 12 4 3 L0 L2 L3 0 0

64. End of slot 1 12 4 3 L0 L2 L3 1 01 Low priority to L2

65. End of slot 2 12 4 3 L0 L2 L3 1 0 2 2 2 Low priority to L2

66. End of slot 3 12 4 3 L0 L2 L3 1 0 2 2 3 3 Low priority to L2

67. End of slot 4 12 4 3 L0 L2 L3 1 0 4 2 3 4 4 2  Traffic not stabilized  High priority to L2 will stabilize this

68. Throughput-Optimal Scheduler  A scheduler is throughput-optimal if it can serve all schedulable traffic [Tassiulas92] Schedule = arg max ∑ ri qi Load 1 Load 2

69. Throughput-Optimal CSMA (Carrier-Sense Multiple Access)  Continuous-time CSMA-like algorithm shown to achieve stability [Jiang-Walrand’08]  Extended to discrete-time CSMA-like algorithms in later work CSMA model: A link can sense conflicting transmissions

70. 70 CSMA model: A link can sense conflicting transmissions 12 4 3 L0 L2 L3

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72. Imperfect Carrier Sensing 72  Conflicting transmissions may not always be sensed, potentially leading to collisions

73. Imperfect Carrier Sensing  Stability with imperfect carrier sensing ?  Yes, almost 73

74. Proposed CSMA Algorithm Two access probability:  a : probability with which a node attempts to transmit first packet in a “train”  p : probability with which a “train” is extended 74

75. DATA Scheduling Example probe ACK DATA probe Access by a A Access by a B Access by p B Sensed busy by Link A & C Preempted by Link B Sensed idle by Link A & C probe ACK DATA probe ACK DATA Preempted by Link A & C probe BA ABCABC A and C may transmit together

76. With CSMA Failure probe ACK probe Access by a A Access by a B Access by p B Sensed busy by Link A & C Preempted by Link B Sensed idle by Link A & C CSMA failure at B probe DATA BA probe ACK DATA probe ACK DATA ABCABC A and C may transmit together

77. Stability with Sensing Failure  Small enough access probability (a) suffices to stabilize arbitrarily large fraction of rate region  Continuation probability (p) being function of queue size 77

78. Open Problems  Carrier sensing failures … correlation over time and space  Asymmetric collisions  Dynamic adaptation to time-varying channel 78

79. What does this have to do with distributed algorithms ? 79

80. Network stability  No semantics attached to bits  Traffic patterns weakly constrained  Distributed congestion control  Awareness of algorithm’s objective  Traffic completely specified by the algorithm  Distributed control ? 80 Distributed algorithms

81. Can the gap be bridged?  Multi-party algorithms that dynamically adapt to network characteristics 81 Communications / Networking Distributed Algorithms

82. Can the gap be bridged?  Theory versus practice: How to exploit the diversity?  Unknowns in practice (unknown unknowns as well) 82 Communications / Networking Distributed Algorithms

83. Thanks! www.crhc.illinois.edu / wireless

84. Thanks! www.crhc.illinois.edu / wireless

85.  Goal: Agreement on a large file 85 File Message Separate instance of “mini”-algorithm for each message

86. Back-up slides 86

87. BA complexity for sum-rate constraint  Goal: Agreement on a large file 87 File Message (n-f) data symbols (2n-2, n-f) code

88. 2 2 2 1 1 88 n-1 receivers 2(n-1) symbol codeword of dimension n-f

89. Algorithm Outline 89 Initial machine M0 M1 Mmax No more failures time O(n)

90. CSMA 90

91. Scheduling Objective  Network stability L2 L3 L0 Rate region characterized by conflict graph 12 4 3 L0 L2 L3 Network

92. Throughput-Optimal Scheduler  Schedule = arg max ∑ qi (for constant r) max ( q0+q3, q2)  Centralized scheduler 12 4 3 L0 L2 L3

93. Channel Access Model Last α -duration of each time slot for carrier sense Access probability a Continuation probability p

94. Preemptive CSMA  Two access probabilities: a i and p i Carrier sense u(t): preemption x(t): transmission schedule C i : set of conflict links of i ACK reception

95. Carrier Sense Failure: Main Result  By choosing small enough access probability, possible to stabilize arbitrarily large fraction of capacity region Proof complexity: Markov chain is no longer reversible Use perturbation theory for Markov chains