1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer...

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Network-Aware Distributed Algorithmsfor Wireless Networks

Nitin VaidyaElectrical and Computer Engineering

University of Illinois at Urbana-Champaign

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Multi-Channel Wireless Networks:

Theory to Practice

Nitin VaidyaElectrical and Computer Engineering

University of Illinois at Urbana-Champaign

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Wireless Networks

Infrastructure-Based Networks

Infrastructure-Less (and Hybrid) Networks:

– Mesh networks, ad hoc networks, sensor networks

What Makes Wireless Networks Interesting?

Broadcast channel Interference management non-trivial Signal-interference are relative notions

AB C

D

po

we

r Signal Interference

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What Makes Wireless Networks Interesting?

Many forms of diversity

•Time

•Route

•Antenna

•Path

•Channel

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What Makes Wireless Networks Interesting?

Antenna diversity

C

D

A

B

Sidelobes not shown

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What Makes Wireless Networks Interesting?

Path diversity

x1 x2

y1 y2

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What Makes Wireless Networks Interesting?

Channel diversity

AB

AB

Low gain

High gain

AB C

D

AB C

D

Low interference

High interference

Research Challenge

Dynamic adaptation

to exploit available

diversity

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11

Net-X

Multi-Channel Wireless

Mesh

Theory to

Practice

Multi-channelprotocol

Channel Abstraction Module

IP Stack

InterfaceDevice Driver

User Applications

ARP

InterfaceDevice Driver

OS improvementsSoftware architecture

Capacity &Scheduling

channels

capaci

tyA

B

C

D

EF

Fixed

Switchable

Insights onprotocol design

Net-Xtestbed

12

Secret to happiness is to lower your expectations to the point where they're already met

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with apologies to Bill Watterson (Calvin & Hobbes)

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Network-Aware Distributed Algorithmsfor Wireless Networks

Nitin VaidyaElectrical and Computer Engineering

University of Illinois at Urbana-Champaign

Distributed Algorithms & Communications

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Communications / Networking

Distributed Algorithms

Distributed Algorithms & Communications

Problems with overlapping scope

But cultures differ

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Communications / Networking

Distributed Algorithms

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DistributedAlgorithms

Black box networks

Emphasis onorder complexity

Emphasis on “exact”performance metrics

Constants matter

Communications / Networking

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DistributedAlgorithms

Black box networks

Emphasis onorder complexity

Emphasis on “exact”performance metrics

Constants matter

Information transfer(typically “raw” info)

Communications / Networking

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DistributedAlgorithms

Computationaffects communication

Emphasis on “exact”performance metrics

Constants matter

Information transfer(typically “raw” info)

Communications / Networking

Black box networks

Emphasis onorder complexity

Distributed Algorithms & Communications

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Communications / Networking

Distributed Algorithms

Outline

Two distributed algorithms

Byzantine agreement

Scheduling (CSMA)

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Rate Region

Communications / Networking

Distributed Algorithms

Rate Region

Defines the way links may share channel

Interference posed to each other

determines whether a set of links

should be active together

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“Ethernet” Rate Region

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S

1 2

Rate S1 + Rate S2 ≤ C

R1 + R2 ≤ C

Private channelsS1 and S2

Rate S1

Rate S2

sum-rateconstraint

Point-to-Point NetworkRate Region

Rij ≤ Capacity ij

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S

1 2

Each directed linkindependent of other links

Wireless Network: Rate Region

Some links share channel with each otherwhile others don’t

1 2 43R1 R2 R3

max(R1/C1 , R3/C3) + (R2/C2) ≤ 1

Broadcast Channel:Rate Region

R ≤ C1

S

2

3

1

Broadcast Channel:Rate Region

> C1

S

2

3

R ≤ C2

“Range” varies inverselywith rate

1

Broadcast Channel

S2

3

1

S

2

3

1

R1 R2

R12

R1/C1 + R2/C2 + R12/C12 ≤ 1

Outline

Two distributed algorithms

Byzantine agreement

Scheduling (CSMA)

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Impact of Rate Region

Network rate region affects

ability to perform

multi-party computation

Example:Byzantine agreement (broadcast)

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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

Impact of Rate Region

How does rate region affect

broadcast performance ?

How to quantify the impact ?

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Throughput of Agreement

Borrow notion of throughput

from communications literature

b(t) = number of bits agreed upon in [0,t]

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t

tbThroughput

t

)(lim

Long timescale measure

Capacity of Agreement

Supremum of achievable throughputs

for a given rate region

Broadcast Channel

Rate region R ≤ C

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Agreement capacity = CS

2

3

1

R

“Ethernet” Rate Region

Sum ofprivate link capacities ≤ C

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Agreement capacity = C

Communication complexityper agreed bit

1

S

2

3

“Ethernet” Rate Region

Communication complexity per-agreed bit

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L

number of bits required to agree on L bits=

“Ethernet” Rate Region

Communication complexity per-agreed bit

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L

number of bits required to agree on L bits=

“Ethernet” Rate Region

Communication complexity per-agreed bit

L = 1 : Ω(n2) for n node [Dolev-Reischuk] (deterministic

algorithms)

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L

number of bits required to agree on L bits=

“Ethernet” Rate Region

Communication complexity per-agreed bit

L = 1 : Ω(n2) for n nodes

L ∞ : can be shown O(n) (multi-value agreement)

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L

number of bits required to agree on L bits=

“Ethernet” Rate Region

Communication complexity per-agreed bit

L = 1 : Ω(n2) for n nodes

L ∞ : can be shown O(n) (multi-value agreement)

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L

number of bits required to agree on L bits=

41bits per agreed-bit n(n-1)(n-f)

“Ethernet” Rate Region

Sum ofprivate link capacities ≤ C

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Agreement capacity ≥ Cn(n-1)

(n-f)

Conjecture: tight bound

1

S

2

3

A

S

B

C

Point-to-Point Network

Each link has itsown capacity

Load ij ≤ Cij

A

S

B

C

4

2

4

3 344

3

3

Point-to-Point Network

Each link has itsown capacity

Cij as shown

AgreementCapacity ?

Point-to-Point Network

Cij as shown

AgreementCapacity = 2

A

S

B

C

4

2

4

3 344

3

3

Point-to-Point Network

є

Cij as shown

AgreementCapacity = 6

A

S

B

C

4

2

4

3 344

3

3

A

S

B

C

Point-to-Point Network

Capacity-achievingscheme for

Arbitrary 4 nodenetworks

Approach:Upper boundbased on min-cutsLower bound usingcoding

A

S

B

C

Point-to-Point Network

Capacity-achievingscheme for

Arbitrary 4 nodenetworks

Minimum numberof rounds requireddepends on linkcapacities

A

S

B

C

Point-to-Point Network

Open problem:

Everything else

Capacity-achievingscheme for

Arbitrary 4 nodenetworks

Open Problems

Capacity-achieving agreement withgeneral rate regions

Subset of nodes as “receivers”

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Open Problems

Capacity-achieving agreement withgeneral rate regions

Subset of nodes as “receivers”

Even the multicast problem with Byzantine nodes is unsolved

- For multicast, source S fault-free51

Rich Problem Space

Broadcast channel allows overhearing

Transmit to 2 at highrate, or low rate ?

- Low rate allows reception at 1

(broadcast advantage)

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S

2

3

1

Rich Problem Space

Broadcast channel allows overhearing

Transmit to 2 at highrate, or low rate ?

- Low rate allows reception at 1

(broadcast advantage)

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S

2

3

1

Low rate

Rich Problem Space

Broadcast channel allows overhearing

Transmit to 2 at highrate, or low rate ?

- Low rate allows reception at 1

(broadcast advantage)

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S

2

3

1

High rate

Rich Problem Space

How to model & exploit receptionwith probability < 1 ?

– Need opportunistic algorithms

Use of available diversity affects rate region

– How to dynamically adapt to channel variations ?

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Rich Problem Space

Similar questions relevant for anymulti-party computation

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Communications / Networking

Distributed Algorithms

And Now for Something Completely Different *

* Monty Python

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Outline

Two distributed algorithms

Byzantine agreement

Scheduling (CSMA)

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Scheduling Objective

Network stability

1 2 43L0 L2 L3

Scheduling Objective

Network stability

1 2 43L0 L2 L3

1 2 43L0 L2 L3

Scheduling

1 2 43L0 L2 L3

1/2 1/21/2Arrivalrates

1 2 43L0 L2 L3

Arrivalsin even slots

Arrivalsin odd slots

End of slot 0

1 2 43L0 L2 L3

0 0

End of slot 1

1 2 43L0 L2 L3

1

0 1

Lowpriorityto L2

End of slot 2

1 2 43L0 L2 L3

1

0

2

2

2

Lowpriorityto L2

End of slot 3

1 2 43L0 L2 L3

1

0

2

2

3

3

Lowpriorityto L2

End of slot 4

1 2 43L0 L2 L3

1

0

4

2

3

4

4

2

Traffic not stabilized High priority to L2 will stabilize this

Throughput-Optimal Scheduler

A scheduler is throughput-optimal ifit can serve all schedulable traffic [Tassiulas92]

Schedule = arg max ∑ ri qi

Load 1

Load 2

Throughput-OptimalCSMA (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

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CSMA model:A link can sense conflicting transmissions

1 2 43L0 L2 L3

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Imperfect Carrier Sensing

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Conflicting transmissions may not always be sensed,

potentially leading to collisions

Imperfect Carrier Sensing

Stability with imperfect carrier sensing ?

Yes, almost

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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

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DATA

Scheduling Example

probe

ACK

DATA

probe

Access by aA

Access by aB

Access by aB

Access by pB

Sensed busy by Link A &

C

Preempted by Link

B

Sensed idle by

Link A & C

probe

ACK

DATA

probe

ACK

DATA DATA

Preempted by Link A

& C

probe BA

A

B

C

A and C may transmit together

With CSMA Failure

probe

ACK

probe

Access by aA

Access by aB

Access by aB

Access by pB

Sensed busy by Link A &

C

Preempted by Link

B

Sensed idle by

Link A & C

CSMA failure at B

probe

probe

DATA BA

probe

ACK

DATA

probe

ACK

DATA DATA

DATA

A

B

C

A and C may transmit together

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

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Open Problems

Carrier sensing failures …correlation over time and space

Asymmetric collisions

Dynamic adaptation to time-varying channel

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What does this have to do with

distributed algorithms ?

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Networkstability

No semanticsattached to bits

Traffic patterns weakly constrained

Distributed congestion control

Awareness of algorithm’s objective

Traffic completely specified by the algorithm

Distributed control ?

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Distributed algorithms

Can the gap be bridged?

Multi-party algorithms that dynamically adapt to

network characteristics

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Communications / Networking

Distributed Algorithms

Can the gap be bridged?

Theory versus practice: How to exploit the diversity?

Unknowns in practice

(unknown unknowns as well)

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Communications / Networking

Distributed Algorithms

Thanks!

www.crhc.illinois.edu / wireless

Thanks!

www.crhc.illinois.edu / wireless

Goal: Agreement on a large file

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File

Message

Separate instance of “mini”-algorithm for each message

Back-up slides

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BA complexity for sum-rate constraint

Goal: Agreement on a large file

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File

Message

(n-f) data symbols

(2n-2, n-f) code

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2

1

1

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n-1 receivers

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

Algorithm Outline

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Initialmachine

M0M1 Mma

x No more failures

time

O(n) O(n) O(n) O(n)

CSMA

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Scheduling Objective

Network stability

L2

L3L0 Rate regioncharacterized by

conflict graph

1 2 43L0 L2 L3

Network

Throughput-Optimal Scheduler

Schedule = arg max ∑ qi (for constant r)

max ( q0+q3, q2)

Centralized scheduler

1 2 43L0 L2 L3

Channel Access Model

Last α-duration of each time slot for carrier sense

Accessprobability a

Continuationprobability p

Preemptive CSMA

Two access probabilities: ai and pi

Carrier sense

u(t): preemptionx(t): transmission scheduleCi: set of conflict links of i

ACK reception

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 Markovchains