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

1

Network-Aware Distributed Algorithmsfor Wireless Networks

Nitin VaidyaElectrical and Computer Engineering

University of Illinois at Urbana-Champaign

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3

Multi-Channel Wireless Networks:

Theory to Practice



4

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

6


Many forms of diversity

•Time

•Route

•Antenna

•Path

•Channel

7


Antenna diversity

C

D

A

B

Sidelobes not shown

8


Path diversity

x1 x2

y1 y2

9


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

10

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

13

with apologies to Bill Watterson (Calvin & Hobbes)

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Network-Aware Distributed Algorithmsfor Wireless Networks



Distributed Algorithms & Communications

15

Communications / Networking

Distributed Algorithms


Problems with overlapping scope

But cultures differ

16



17

DistributedAlgorithms

Black box networks

Emphasis onorder complexity

Emphasis on “exact”performance metrics

Constants matter


18


Black box networks



Constants matter

Information transfer(typically “raw” info)


19


Computationaffects communication


Constants matter

Information transfer(typically “raw” info)


Black box networks



20



Outline

Two distributed algorithms

Byzantine agreement

Scheduling (CSMA)

21

Rate Region



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

“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

24

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


Byzantine agreement

Scheduling (CSMA)

29

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 ?

32

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


Sum ofprivate link capacities ≤ C

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Agreement capacity = C

Communication complexityper agreed bit

1

S

2

3


Communication complexity per-agreed bit

37

L

number of bits required to agree on L bits=



38

L




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

algorithms)

39

L




L = 1 : Ω(n2) for n nodes

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

40

L




L = 1 : Ω(n2) for n nodes

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

41

L


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


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


Each link has itsown capacity

Cij as shown

AgreementCapacity ?


Cij as shown

AgreementCapacity = 2

A

S

B

C

4

2

4

3 344

3

3


є

Cij as shown

AgreementCapacity = 6

A

S

B

C

4

2

4

3 344

3

3

A

S

B

C


Capacity-achievingscheme for

Arbitrary 4 nodenetworks

Approach:Upper boundbased on min-cutsLower bound usingcoding

A

S

B

C




Minimum numberof rounds requireddepends on linkcapacities

A

S

B

C


Open problem:

Everything else



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





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S

2

3

1

Low rate

Rich Problem Space





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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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And Now for Something Completely Different *

* Monty Python

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Outline


Byzantine agreement

Scheduling (CSMA)

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Scheduling Objective

Network stability

1 2 43L0 L2 L3


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 ?

80

Distributed algorithms

Can the gap be bridged?

Multi-party algorithms that dynamically adapt to

network characteristics

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Can the gap be bridged?

Theory versus practice: How to exploit the diversity?

Unknowns in practice

(unknown unknowns as well)

82



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

86

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

22

2

1

1

88

n-1 receivers

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

Algorithm Outline

89

Initialmachine

M0M1 Mma

x No more failures

time

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

CSMA

90


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

Documents

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