NetworkAware Distributed Algorithms for Wireless Networks Nitin Vaidya

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

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

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

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

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

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

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

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

Research Challenge Dynamic adaptation to exploit available diversity 10

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

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

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

Distributed Algorithms & Communications / Networking Distributed Algorithms 15

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

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

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

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

Distributed Algorithms & Communications / Networking Distributed Algorithms 20

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

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

“Ethernet” Rate Region S 1 sum-rate constraint Rate S 2 2 Rate S 1 Private channels S 1 and S 2 + Rate S 2 ≤ C R 1 + R 2 ≤ C Rate S 1 23

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

Wireless Network: Rate Region g Some links share channel with each other while others don’t 1 R 1 2 R 2 3 R 3 max(R 1/C 1 , R 3/C 3) + (R 2/C 2) 4 ≤ 1

Broadcast Channel: Rate Region 1 R ≤ C 1 2 S 3

Broadcast Channel: Rate Region 1 R ≤ C 2 > C 1 2 S 3 “Range” varies inversely with rate

Broadcast Channel 1 1 S 2 R 1 3 2 S R 2 3 R 1/C 1 + R 2/C 2 + R 12/C 12 ≤ 1 R 12

Outline Two distributed algorithms g Byzantine agreement g Scheduling (CSMA) 29

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

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

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

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

Capacity of Agreement g Supremum of achievable throughputs for a given rate region

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Open Problems g g g 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

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

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

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

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

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

And Now for Something Completely Different * * Monty Python 57

Outline Two distributed algorithms g Byzantine agreement g Scheduling (CSMA) 58

Scheduling Objective g Network stability 1 L 0 2 L 2 3 L 3 4

Scheduling Objective g Network stability 1 1 L 0 2 2 L 2 3 3 L 3 4 4

Scheduling Arrival rates 1/2 1 L 0 2 1/2 L 3 3 4

Arrivals in odd slots Arrivals in even slots 1 L 0 2 L 2 3 L 3 4

End of slot 0 1 0 0 L 2 2 3 L 3 4

End of slot 1 0 1 L 0 2 L 2 1 3 L 3 4 1 Low priority to L 2

End of slot 2 1 2 2 0 L 2 1 2 3 L 3 4 2 Low priority to L 2

End of slot 3 1 L 0 3 1 2 2 0 3 L 2 L 3 3 4 2 Low priority to L 2

End of slot 4 1 4 4 2 0 L 2 2 3 L 3 4 4 2 3 1 g g Traffic not stabilized High priority to L 2 will stabilize this

Throughput-Optimal Scheduler g A scheduler is throughput-optimal if it can serve all schedulable traffic Schedule = arg max ∑ ri qi Load 2 Load 1 [Tassiulas 92]

Throughput-Optimal CSMA (Carrier-Sense Multiple Access) g g 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

1 L 0 2 L 2 3 L 3 4 CSMA model: A link can sense conflicting transmissions 70

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

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

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

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

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

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

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

What does this have to do with distributed algorithms ? 79

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

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

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

Thanks! www. crhc. illinois. edu / wireless

Thanks! www. crhc. illinois. edu / wireless

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

Back-up slides 86

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

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

Algorithm Outline failure diagnosis O(n 2 diagnosis ) failure O(n 2) diagnosis O(n 2) O(n) Initial machine M 0 M 1 time Mmax No more failures 89

CSMA 90

Scheduling Objective g Network stability 1 L 0 2 L 2 3 L 0 L 2 L 3 4 Network Rate region characterized by conflict graph

Throughput-Optimal Scheduler g Schedule = arg max ∑ qi 1 L 0 2 L 2 3 (for constant r) L 3 4 max ( q 0+q 3, q 2) g Centralized scheduler

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

Preemptive CSMA Carrier sense u(t): preemption x(t): transmission schedule Ci: set of conflict links of i ACK reception g Two access probabilities: ai and pi

Carrier Sense Failure: Main Result g 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