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![Page 1: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/1.jpg)
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Network-Aware Distributed Algorithmsfor Wireless Networks
Nitin VaidyaElectrical and Computer Engineering
University of Illinois at Urbana-Champaign
![Page 2: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/2.jpg)
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Multi-Channel Wireless Networks:
Theory to Practice
Nitin VaidyaElectrical and Computer Engineering
University of Illinois at Urbana-Champaign
![Page 4: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/4.jpg)
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Wireless Networks
Infrastructure-Based Networks
Infrastructure-Less (and Hybrid) Networks:
– Mesh networks, ad hoc networks, sensor networks
![Page 5: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/5.jpg)
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
![Page 10: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/10.jpg)
Research Challenge
Dynamic adaptation
to exploit available
diversity
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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
![Page 12: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/12.jpg)
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Secret to happiness is to lower your expectations to the point where they're already met
13
with apologies to Bill Watterson (Calvin & Hobbes)
![Page 14: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/14.jpg)
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Network-Aware Distributed Algorithmsfor Wireless Networks
Nitin VaidyaElectrical and Computer Engineering
University of Illinois at Urbana-Champaign
![Page 15: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/15.jpg)
Distributed Algorithms & Communications
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Communications / Networking
Distributed Algorithms
![Page 16: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/16.jpg)
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
![Page 18: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/18.jpg)
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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
![Page 19: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/19.jpg)
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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
![Page 20: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/20.jpg)
Distributed Algorithms & Communications
20
Communications / Networking
Distributed Algorithms
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Outline
Two distributed algorithms
Byzantine agreement
Scheduling (CSMA)
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Rate Region
Communications / Networking
Distributed Algorithms
![Page 22: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/22.jpg)
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
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Point-to-Point NetworkRate Region
Rij ≤ Capacity ij
24
S
1 2
Each directed linkindependent of other links
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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
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Broadcast Channel:Rate Region
R ≤ C1
S
2
3
1
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Broadcast Channel:Rate Region
> C1
S
2
3
R ≤ C2
“Range” varies inverselywith rate
1
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Broadcast Channel
S2
3
1
S
2
3
1
R1 R2
R12
R1/C1 + R2/C2 + R12/C12 ≤ 1
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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
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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]
33
t
tbThroughput
t
)(lim
Long timescale measure
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Capacity of Agreement
Supremum of achievable throughputs
for a given rate region
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Broadcast Channel
Rate region R ≤ C
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Agreement capacity = CS
2
3
1
R
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“Ethernet” Rate Region
Sum ofprivate link capacities ≤ C
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Agreement capacity = C
Communication complexityper agreed bit
1
S
2
3
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“Ethernet” Rate Region
Communication complexity per-agreed bit
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L
number of bits required to agree on L bits=
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“Ethernet” Rate Region
Communication complexity per-agreed bit
38
L
number of bits required to agree on L bits=
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“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=
![Page 40: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/40.jpg)
“Ethernet” Rate Region
Communication complexity per-agreed bit
L = 1 : Ω(n2) for n nodes
L ∞ : can be shown O(n) (multi-value agreement)
40
L
number of bits required to agree on L bits=
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“Ethernet” Rate Region
Communication complexity per-agreed bit
L = 1 : Ω(n2) for n nodes
L ∞ : can be shown O(n) (multi-value agreement)
41
L
number of bits required to agree on L bits=
41bits per agreed-bit n(n-1)(n-f)
![Page 42: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/42.jpg)
“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
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A
S
B
C
Point-to-Point Network
Each link has itsown capacity
Load ij ≤ Cij
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A
S
B
C
4
2
4
3 344
3
3
Point-to-Point Network
Each link has itsown capacity
Cij as shown
AgreementCapacity ?
![Page 45: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/45.jpg)
Point-to-Point Network
Cij as shown
AgreementCapacity = 2
A
S
B
C
4
2
4
3 344
3
3
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Point-to-Point Network
є
Cij as shown
AgreementCapacity = 6
A
S
B
C
4
2
4
3 344
3
3
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A
S
B
C
Point-to-Point Network
Capacity-achievingscheme for
Arbitrary 4 nodenetworks
Approach:Upper boundbased on min-cutsLower bound usingcoding
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A
S
B
C
Point-to-Point Network
Capacity-achievingscheme for
Arbitrary 4 nodenetworks
Minimum numberof rounds requireddepends on linkcapacities
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A
S
B
C
Point-to-Point Network
Open problem:
Everything else
Capacity-achievingscheme for
Arbitrary 4 nodenetworks
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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
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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
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Rich Problem Space
Broadcast channel allows overhearing
Transmit to 2 at highrate, or low rate ?
- Low rate allows reception at 1
(broadcast advantage)
53
S
2
3
1
Low rate
![Page 54: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/54.jpg)
Rich Problem Space
Broadcast channel allows overhearing
Transmit to 2 at highrate, or low rate ?
- Low rate allows reception at 1
(broadcast advantage)
54
S
2
3
1
High rate
![Page 55: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/55.jpg)
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
![Page 57: 1 Network-Aware Distributed Algorithms for Wireless Networks Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ec55503460f94bcfe43/html5/thumbnails/57.jpg)
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
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Scheduling Objective
Network stability
1 2 43L0 L2 L3
1 2 43L0 L2 L3
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Scheduling
1 2 43L0 L2 L3
1/2 1/21/2Arrivalrates
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1 2 43L0 L2 L3
Arrivalsin even slots
Arrivalsin odd slots
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End of slot 0
1 2 43L0 L2 L3
0 0
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End of slot 1
1 2 43L0 L2 L3
1
0 1
Lowpriorityto L2
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Traffic not stabilized High priority to L2 will stabilize this
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Throughput-Optimal Scheduler
A scheduler is throughput-optimal ifit can serve all schedulable traffic [Tassiulas92]
Schedule = arg max ∑ ri qi
Load 1
Load 2
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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
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Imperfect Carrier Sensing
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Conflicting transmissions may not always be sensed,
potentially leading to collisions
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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
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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
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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
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Can the gap be bridged?
Multi-party algorithms that dynamically adapt to
network characteristics
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Communications / Networking
Distributed Algorithms
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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
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Thanks!
www.crhc.illinois.edu / wireless
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Thanks!
www.crhc.illinois.edu / wireless
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Goal: Agreement on a large file
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File
Message
Separate instance of “mini”-algorithm for each message
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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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22
2
1
1
88
n-1 receivers
2(n-1) symbol codeword of dimension n-f
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Algorithm Outline
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Initialmachine
M0M1 Mma
x No more failures
time
O(n) O(n) O(n) O(n)
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CSMA
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Scheduling Objective
Network stability
L2
L3L0 Rate regioncharacterized by
conflict graph
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Network
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Throughput-Optimal Scheduler
Schedule = arg max ∑ qi (for constant r)
max ( q0+q3, q2)
Centralized scheduler
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Channel Access Model
Last α-duration of each time slot for carrier sense
Accessprobability a
Continuationprobability p
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Preemptive CSMA
Two access probabilities: ai and pi
Carrier sense
u(t): preemptionx(t): transmission scheduleCi: set of conflict links of i
ACK reception
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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