Problem and Objectives
Background
NUM with packet corruption
Examples
Rate Control with Packet Corruption
David Hayes
david.hayes@ieee.org
Joint work the Lachlan Andrew
CSIRO ICT Centre, Marsfield, 27 August 2007
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
1/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Outline
1
Problem and Objectives
2
Background
3
NUM with packet corruption
4
Examples
5
Conclusions and further work
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
2/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
What do we mean by corruption?
Information either completely lost, or partially lost.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
What do we mean by corruption?
Information either completely lost, or partially lost.
Wireless links can have very high corruption rates
eg Sensor Networks
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
What do we mean by corruption?
Information either completely lost, or partially lost.
Wireless links can have very high corruption rates
eg Sensor Networks
Why is it bad?
Reduction in end-user utility
TCP treats corruption loss as congestion loss
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
What do we mean by corruption?
Information either completely lost, or partially lost.
Wireless links can have very high corruption rates
eg Sensor Networks
Why is it bad?
Reduction in end-user utility
TCP treats corruption loss as congestion loss
What can be done?
FEC — adaptive?
Layer 2 correction
Transport layer correction
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Examples
Corruption close to source
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Examples
Corruption close to source
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Examples
Corruption close to source
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Objectives
Corruption and optimal fluid based congestion control.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Objectives
Corruption and optimal fluid based congestion control.
What is a fair transmission rate?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Objectives
Corruption and optimal fluid based congestion control.
What is a fair transmission rate?
Look at different ideas of fairness.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Problem
At what rate should traffic sources send when experiencing packet
corruption along their path?
Objectives
Corruption and optimal fluid based congestion control.
What is a fair transmission rate?
Look at different ideas of fairness.
Propose this as an objective for TCP modifications.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
3/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
ICCRG and IETF
Internet Congestion Control Research Group (ICCRG)
How should TCP be adapted to suit the evolving Internet.
TCP’s rate when there is loss due to corruption.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
4/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
ICCRG and IETF
Internet Congestion Control Research Group (ICCRG)
How should TCP be adapted to suit the evolving Internet.
TCP’s rate when there is loss due to corruption.
The Datagram Congestion Control Protocol (DCCP).
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
4/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
Network chooses source rates xs based on ws
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
Network chooses source rates xs based on ws
Low and Lapsley [Low99] solve the same optimisation problem
in a different way:
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
Network chooses source rates xs based on ws
Low and Lapsley [Low99] solve the same optimisation problem
in a different way:
User choose a send rate xs given path cost qs .
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
Network chooses source rates xs based on ws
Low and Lapsley [Low99] solve the same optimisation problem
in a different way:
User choose a send rate xs given path cost qs .
Network chooses a price for each link pl based on congestion.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
Network chooses source rates xs based on ws
Low and Lapsley [Low99] solve the same optimisation problem
in a different way:
User choose a send rate xs given path cost qs .
Network chooses a price for each link pl based on congestion.
Distributed optimisation.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Price based rate control
[Kelly97] developed an optimisation model to investigate
pricing on broadband networks.
Network and User sub-problems
User chooses a willingness to pay ws based on a price.
Network chooses source rates xs based on ws
Low and Lapsley [Low99] solve the same optimisation problem
in a different way:
User choose a send rate xs given path cost qs .
Network chooses a price for each link pl based on congestion.
Distributed optimisation.
Since this work NUM has been applied to a many network
protocols (see [Chiang07])
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
5/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Basic NUM
max
X
Us (xs ) subject to Rx ≤ C
s
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
6/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Background
Basic NUM
max
X
Us (xs ) subject to Rx ≤ C
s
Maximise the sum of all source utilities, subject to capacity
U(xs )
xs
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
6/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Each source, s, solves:
xs = (Us0 )−1 (qs ), where qs =
X
rls pl , and Us its utility.
l
Note R = rls , the route matrix, rls = 1 if source s uses link l.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
7/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Each source, s, solves:
xs = (Us0 )−1 (qs ), where qs =
X
rls pl , and Us its utility.
l
Network sub-problem
∂L(x, p) X
=
rls xs − cl = 0
∂pl
s
∀l.
Price pl = 0 if no congestion and pl > 0 if congestion.
Note R = rls , the route matrix, rls = 1 if source s uses link l.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
7/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Mo’s and Warland’s α-fair utilities
Mo’s and Warland’s [Mo00] α-fair utility family:
xs = U 0 (qs ) = qs−α
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
(1)
8/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Mo’s and Warland’s α-fair utilities
Mo’s and Warland’s [Mo00] α-fair utility family:
xs = U 0 (qs ) = qs−α
(1)
Where:
α = 1 yields Kelly’s proportional, fairness [Kelly98],
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
8/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Mo’s and Warland’s α-fair utilities
Mo’s and Warland’s [Mo00] α-fair utility family:
xs = U 0 (qs ) = qs−α
(1)
Where:
α = 1 yields Kelly’s proportional, fairness [Kelly98],
α → ∞ yields max-min fairness,
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
8/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Mo’s and Warland’s α-fair utilities
Mo’s and Warland’s [Mo00] α-fair utility family:
xs = U 0 (qs ) = qs−α
(1)
Where:
α = 1 yields Kelly’s proportional, fairness [Kelly98],
α → ∞ yields max-min fairness,
α → 0 sources become less sensitive to price changes,
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
8/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
ICCRG and IETF
Price based rate control
Network Utility Maximisation Framework
α-fair utilities
Mo’s and Warland’s α-fair utilities
Mo’s and Warland’s [Mo00] α-fair utility family:
xs = U 0 (qs ) = qs−α
(1)
Where:
α = 1 yields Kelly’s proportional, fairness [Kelly98],
α → ∞ yields max-min fairness,
α → 0 sources become less sensitive to price changes,
α = 2 approximates TCP fairness [Massoulie02].
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
8/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
A traffic source, s, sending data at rate xs has a fraction s
corrupted by the network.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
9/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
A traffic source, s, sending data at rate xs has a fraction s
corrupted by the network.
The utility of source s is now:
U(xs ; s )
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
9/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
A traffic source, s, sending data at rate xs has a fraction s
corrupted by the network.
The utility of source s is now:
U(xs ; s )
If corrupt packets contain no information
Source s, transmitting at rate xs only achieves utility for xs (1 − s ):
U(xs ; s ) = U(xs (1 − s ); 0).
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
9/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Some assumptions
Fluid flow (general NUM).
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
10/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Some assumptions
Fluid flow (general NUM).
Sources see Link price in proportion to their rate (general
NUM)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
10/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Some assumptions
Fluid flow (general NUM).
Sources see Link price in proportion to their rate (general
NUM)
pl = 0 when link underutilised, pl > 0 when congestion.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
10/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Some assumptions
Fluid flow (general NUM).
Sources see Link price in proportion to their rate (general
NUM)
pl = 0 when link underutilised, pl > 0 when congestion.
Probability of corruption is independent of congestion.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
10/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Some assumptions
Fluid flow (general NUM).
Sources see Link price in proportion to their rate (general
NUM)
pl = 0 when link underutilised, pl > 0 when congestion.
Probability of corruption is independent of congestion.
Greedy sources.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
10/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If corrupt packets travel through the network and use capacity
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
11/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If corrupt packets travel through the network and use capacity
Calculation of pl will not change
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
11/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If corrupt packets travel through the network and use capacity
Calculation of pl will not change
It follows then:
xs = (Us0 )−1 (qs ; s )
1
qs
0 −1
=
(U )
;0 .
1 − s
1 − s
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
11/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
Let r̂ls be the fraction of s’s data that traverses link l.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
Let r̂ls be the fraction of s’s data that traverses link l.
P
The sum of link prices for s is now q̂s = l r̂ls pl and
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
Let r̂ls be the fraction of s’s data that traverses link l.
P
The sum of link prices for s is now q̂s = l r̂ls pl and
q̂s
1
0 −1
0 −1
xs = (U ) (q̂s ; s ) =
(U )
;0 .
1 − s
1 − s
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
(2)
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
Let r̂ls be the fraction of s’s data that traverses link l.
P
The sum of link prices for s is now q̂s = l r̂ls pl and
q̂s
1
0 −1
0 −1
xs = (U ) (q̂s ; s ) =
(U )
;0 .
1 − s
1 − s
(2)
But how does s calculate q̂s ?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
Let r̂ls be the fraction of s’s data that traverses link l.
P
The sum of link prices for s is now q̂s = l r̂ls pl and
q̂s
1
0 −1
0 −1
xs = (U ) (q̂s ; s ) =
(U )
;0 .
1 − s
1 − s
(2)
But how does s calculate q̂s ?
How does s know R̂ = r̂ls ?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
NUM with packet corruption
If the network discards corrupt packets
The network calculates pl based on the thinned traffic.
The path cost for s, is now a weighted sum of pl
Let r̂ls be the fraction of s’s data that traverses link l.
P
The sum of link prices for s is now q̂s = l r̂ls pl and
q̂s
1
0 −1
0 −1
xs = (U ) (q̂s ; s ) =
(U )
;0 .
1 − s
1 − s
(2)
But how does s calculate q̂s ?
How does s know R̂ = r̂ls ?
If s only knows R will xs be very different?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
12/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Using Mo’s and Warland’s α-fair utility (1) with (2):
xs = (1 − s )1/α−1 qˆs −1/α
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
13/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Using Mo’s and Warland’s α-fair utility (1) with (2):
xs = (1 − s )1/α−1 qˆs −1/α
Interpretation
Max-min fairness, α → ∞
Sources with a lower throughput due to s have xs boosted.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
13/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Using Mo’s and Warland’s α-fair utility (1) with (2):
xs = (1 − s )1/α−1 qˆs −1/α
Interpretation
Max-min fairness, α → ∞
Sources with a lower throughput due to s have xs boosted.
Maximum throughput, α → 0
sources with the lowest s receive all the bandwidth.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
13/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Using Mo’s and Warland’s α-fair utility (1) with (2):
xs = (1 − s )1/α−1 qˆs −1/α
Interpretation
Max-min fairness, α → ∞
Sources with a lower throughput due to s have xs boosted.
Maximum throughput, α → 0
sources with the lowest s receive all the bandwidth.
Proportional fairness, α = 1
xs is independent of s .
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
13/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Using Mo’s and Warland’s α-fair utility (1) with (2):
xs = (1 − s )1/α−1 qˆs −1/α
Interpretation
Max-min fairness, α → ∞
Sources with a lower throughput due to s have xs boosted.
Maximum throughput, α → 0
sources with the lowest s receive all the bandwidth.
Proportional fairness, α = 1
xs is independent of s .
If corrupt packets use network capacity q̂s = qs
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
13/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Case 1: Corrupt packets use network capacity
Case 2: Corrupt packets are discarded
Using Mo’s and Warland’s α-fair utilities
Using Mo’s and Warland’s α-fair utility (1) with (2):
xs = (1 − s )1/α−1 qˆs −1/α
Interpretation
Max-min fairness, α → ∞
Sources with a lower throughput due to s have xs boosted.
Maximum throughput, α → 0
sources with the lowest s receive all the bandwidth.
Proportional fairness, α = 1
xs is independent of s .
If corrupt packets use network capacity q̂s = qs
Simple implementation similar to HS-TCP and H-TCP
ŵ = (1 − )1/α−1 w
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
13/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Examples
Example 1 - Simple 4 link network
link 1
link 3
1
2
3
4
1
3
link 2
link 4
2
4
Figure: Simple 4 link, 4 source network
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
14/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Examples
Example 1 - Simple 4 link network
link 1
link 3
1
2
3
4
1
3
link 2
link 4
2
4
Figure: Simple 4 link, 4 source network
Models four different paths, but all are two hops.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
14/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Examples
Example 1 - Simple 4 link network
link 1
link 3
1
2
3
4
1
3
link 2
link 4
2
4
Figure: Simple 4 link, 4 source network
Models four different paths, but all are two hops.
Look at:
Corruption on link 1 and link 3 with half capacity
Corruption on link 3 and link 1 with half capacity
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
14/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 1
1.8
1
2
1.6
3
4
Transmission rate
1.4
2
1
1
3
2
2
2
4
source 1
source 2
source 3
source 4
source 1 at link 3
source 2 at link 4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 1
0.35
0.4
0.45
Figure: Sources ignore loss due to corruption (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
15/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 1
1.8
1
2
1.6
3
4
Transmission rate
1.4
2
1
1
3
2
2
2
4
source 1
source 2
source 3
source 4
source 1 at link 3
source 2 at link 4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 1
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
16/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 3
1.8
1
2
1.6
3
4
Transmission rate
1.4
1
2
1
3
2
2
source 1
source 2
source 3
source 4
2
4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Sources ignore loss due to corruption (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
17/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 3
1.8
1
2
1.6
3
4
Transmission rate
1.4
1
2
1
3
2
2
source 1
source 2
source 3
source 4
2
4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
18/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 3
3.2
Full corruption capability
Sources ignoring corruption
3
Rx rate
2.8
2.6
2.4
2.2
2
1.8
0
0.1
0.2
0.3
0.4
Error rate on link 3
0.5
0.6
Figure: Total received throughput (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
19/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
α = 2 fairness
Sources experiencing corruption have reduced utility.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
20/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
α = 2 fairness
Sources experiencing corruption have reduced utility.
Therefore xs is relatively higher than s = 0 sources.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
20/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
α = 2 fairness
Sources experiencing corruption have reduced utility.
Therefore xs is relatively higher than s = 0 sources.
Network is efficient when corruption is on first hop
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
20/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
α = 2 fairness
Sources experiencing corruption have reduced utility.
Therefore xs is relatively higher than s = 0 sources.
Network is efficient when corruption is on first hop
Network less efficient when corruption is on last hop
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
20/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
α = 2 fairness
Sources experiencing corruption have reduced utility.
Therefore xs is relatively higher than s = 0 sources.
Network is efficient when corruption is on first hop
Network less efficient when corruption is on last hop
Is α = 2 fairness the right balance between end-user utility and
network resource efficiency?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
20/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
α = 2 fairness
Sources experiencing corruption have reduced utility.
Therefore xs is relatively higher than s = 0 sources.
Network is efficient when corruption is on first hop
Network less efficient when corruption is on last hop
Is α = 2 fairness the right balance between end-user utility and
network resource efficiency?
Setting α < 2 shifts the balance toward network efficiency
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
20/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 3
1.8
1
2
1.6
3
4
Transmission rate
1.4
1
2
1
3
2
2
source 1
source 2
source 3
source 4
2
4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 0.8)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
21/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Comparing the characteristics of α = 2 with α = 0.8
1.8
1.8
1
2
1.6
3
4
2
1
3
2
2
source 1
source 2
source 3
source 4
1
2
1.6
2
4
3
4
1.4
Transmission rate
Transmission rate
1.4
1
1.2
1
0.8
0.6
0.4
1
2
1
3
2
2
source 1
source 2
source 3
source 4
2
4
1.2
1
0.8
0.6
0.4
0.2
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 2) and (α = 0.8)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
22/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Comparing the characteristics of α = 2 with α = 0.8
1.8
1.8
1
2
1.6
3
4
2
1
3
2
2
source 1
source 2
source 3
source 4
1
2
1.6
2
4
3
4
1.4
Transmission rate
Transmission rate
1.4
1
1.2
1
0.8
0.6
0.4
1
2
1
3
2
2
source 1
source 2
source 3
source 4
2
4
1.2
1
0.8
0.6
0.4
0.2
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 2) and (α = 0.8)
High α → high throughput fairness
Low α → low throughput fairness
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
22/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 3
3
Full corruption capability
Sources ignoring corruption
2.9
Rx rate
2.8
2.7
2.6
2.5
2.4
2.3
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Total received throughput (α = 0.8)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
23/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 1
1.8
1
2
1.6
3
4
Transmission rate
1.4
2
1
1
3
2
2
2
4
source 1
source 2
source 3
source 4
source 1 at link 3
source 2 at link 4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 1
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 0.8)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
24/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Comparing the characteristics of α = 2 with α = 0.8
1.8
1.8
1
2
1.6
3
4
1
1
3
2
2
2
4
source 1
source 2
source 3
source 4
source 1 at link 3
source 2 at link 4
1.2
1
0.8
0.6
1
2
1.6
3
4
1.4
Transmission rate
Transmission rate
1.4
2
0.4
2
1
2
2
1
3
2
4
source 1
source 2
source 3
source 4
source 1 at link 3
source 2 at link 4
1.2
1
0.8
0.6
0.4
0.2
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 1
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 1
0.35
0.4
0.45
Figure: Sources adapt to corruption (α = 2) and (α = 0.8)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
25/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Interestingly the case with corruption on the first link behaves
similarly for both α = 2 and α = 0.8
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
26/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Interestingly the case with corruption on the first link behaves
similarly for both α = 2 and α = 0.8
Increasing the send rate of sources 1 and 2 also increases the
network efficiency in both cases.
Corrupt packets are dropped at link 1.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
26/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Interestingly the case with corruption on the first link behaves
similarly for both α = 2 and α = 0.8
Increasing the send rate of sources 1 and 2 also increases the
network efficiency in both cases.
Corrupt packets are dropped at link 1.
Also, this is a special case where all flows have two hops.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
26/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Interestingly the case with corruption on the first link behaves
similarly for both α = 2 and α = 0.8
Increasing the send rate of sources 1 and 2 also increases the
network efficiency in both cases.
Corrupt packets are dropped at link 1.
Also, this is a special case where all flows have two hops.
A source’s utility is calculated using sum of link prices along
its path.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
26/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Interestingly the case with corruption on the first link behaves
similarly for both α = 2 and α = 0.8
Increasing the send rate of sources 1 and 2 also increases the
network efficiency in both cases.
Corrupt packets are dropped at link 1.
Also, this is a special case where all flows have two hops.
A source’s utility is calculated using sum of link prices along
its path.
This the dynamic changes when sources travel different
numbers of hops.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
26/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Example 2 - Simple 4 link 8 source network
5
5
7
link 1
7
link 3
1
2
1
3
link 2
3
4
6
link 4
6
8
2
4
8
Figure: Simple 4 link, 8 source network
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
27/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Example 2 - Simple 4 link 8 source network
5
5
7
link 1
7
link 3
1
2
1
3
link 2
3
4
6
link 4
6
8
2
4
8
Figure: Simple 4 link, 8 source network
Models eight different paths of 1 or 2 hop lengths.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
27/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Example 2 - Simple 4 link 8 source network
5
5
7
link 1
7
link 3
1
2
1
3
link 2
3
4
6
link 4
6
8
2
4
8
Figure: Simple 4 link, 8 source network
Models eight different paths of 1 or 2 hop lengths.
Look at:
Corruption on link 1 and link 3 with half capacity
Corruption on link 3 and link 1 with half capacity
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
27/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 1 (subset - link 1)
1.8
5
7
1.5
7
1
3
3
4
1.4
2
4
6
Transmission rate
5
3
1
2
1.6
3
6
8
3
8
1
2
5
1 at 3
2 at 4
5 at 1
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 1
0.35
0.4
0.45
Figure: Sources adapts to corruption (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
28/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Generally even distribution of capacity on all links.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
29/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Generally even distribution of capacity on all links.
Single hop flows have a slight advantage.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
29/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Generally even distribution of capacity on all links.
Single hop flows have a slight advantage.
on link 1 deceases the Us of all flows on the link.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
29/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Generally even distribution of capacity on all links.
Single hop flows have a slight advantage.
on link 1 deceases the Us of all flows on the link.
However, only the two hop flows increase their send rates.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
29/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Generally even distribution of capacity on all links.
Single hop flows have a slight advantage.
on link 1 deceases the Us of all flows on the link.
However, only the two hop flows increase their send rates.
Flows 1 and 2 were restricted by the second hop.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
29/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
Generally even distribution of capacity on all links.
Single hop flows have a slight advantage.
on link 1 deceases the Us of all flows on the link.
However, only the two hop flows increase their send rates.
Flows 1 and 2 were restricted by the second hop.
When link 1 becomes the bottleneck for all three sources
link 1 sources share capacity evenly.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
29/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Corruption loss on link 3
5
5
7
1.5
1
2
7
3
1
3
3
4
1.8
2
4
6
3
6
8
3
1
2
3
4
5
6
7
8
8
1.6
Transmission rate
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Error rate on link 3
0.35
0.4
0.45
Figure: Utility adapts to corruption (α = 2)
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
30/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
2 hop sources with s > 0 lift their relative rates.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
31/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
2 hop sources with s > 0 lift their relative rates.
1 hop source, 7, decreases its rate, so as to fairly share link 3.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
31/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
2 hop sources with s > 0 lift their relative rates.
1 hop source, 7, decreases its rate, so as to fairly share link 3.
Single hop flows have a slight advantage.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
31/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
2 hop sources with s > 0 lift their relative rates.
1 hop source, 7, decreases its rate, so as to fairly share link 3.
Single hop flows have a slight advantage.
Generally –
flows experiencing corruption increase their send rate
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
31/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Example 1 - Simple 4 link 4 source network
Example 2 - Simple 4 link 8 source network
Discussion
2 hop sources with s > 0 lift their relative rates.
1 hop source, 7, decreases its rate, so as to fairly share link 3.
Single hop flows have a slight advantage.
Generally –
flows experiencing corruption increase their send rate
more fairly shares the “goodput” with their competing flows.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
31/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
This work gives a simple way of determining what the fair rate
should be.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
This work gives a simple way of determining what the fair rate
should be.
Can be implemented simply by modifying TCP windows
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
This work gives a simple way of determining what the fair rate
should be.
Can be implemented simply by modifying TCP windows
At the moment there isn’t agreement in the ICCRG about the
user utility/network efficiency balance.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
This work gives a simple way of determining what the fair rate
should be.
Can be implemented simply by modifying TCP windows
At the moment there isn’t agreement in the ICCRG about the
user utility/network efficiency balance.
Depends on:
What service users are paying for.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
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Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
This work gives a simple way of determining what the fair rate
should be.
Can be implemented simply by modifying TCP windows
At the moment there isn’t agreement in the ICCRG about the
user utility/network efficiency balance.
Depends on:
What service users are paying for.
What their use costs network operators.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
Conclusions and further work
Traffic sources should adapt to network corruption fairly.
TCP and DCCP?
This work gives a simple way of determining what the fair rate
should be.
Can be implemented simply by modifying TCP windows
At the moment there isn’t agreement in the ICCRG about the
user utility/network efficiency balance.
Depends on:
What service users are paying for.
What their use costs network operators.
IETF politics.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
32/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
33/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
Packet corruption information?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
33/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
Packet corruption information?
Lower layer indications
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
33/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
Packet corruption information?
Lower layer indications
Indication packets
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
33/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
Packet corruption information?
Lower layer indications
Indication packets
Congestion indication — loss only from corruption
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
33/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
Packet corruption information?
Lower layer indications
Indication packets
Congestion indication — loss only from corruption
Will qs be a good enough approximation of qˆs
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
33/ 33
Problem and Objectives
Background
NUM with packet corruption
Examples
If α > 1 fairness
may need cap for extreme corruption loss.
Packet corruption information?
Lower layer indications
Indication packets
Congestion indication — loss only from corruption
Will qs be a good enough approximation of qˆs
Models for burstiness, TCP-newRENO specifics, real-time
traffic?
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
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Bibliography
M. Chiang, S. H. Low, A. R. Calderbank, and J. C. Doyle.
Layering as optimization decomposition: A mathematical
theory of network architectures.
Proc. IEEE, 95(1):255–312, January 2007.
Frank Kelly.
Charging and rate control for elastic traffic.
European Transactions on Telecommunications, 8:33–37, 1997.
Frank Kelly, Aman Maulloo, and David Tan.
Rate control in communication networks: Shadow prices,
proportional fairness and stability.
J. Op. Res. Soc., 49:237–378, 1998.
S. H. Low and D. E. Lapsley.
Optimization flow control I: Basic algorithm and convergence.
IEEE/ACM Trans. Networking, 7(6):861–875, December 1999.
David Hayes david.hayes@ieee.org
Rate Control with Packet Corruption
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Bibliography
L. Massoulie and J. Roberts.
Bandwidth sharing: objectives and algorithms.
IEEE/ACM Trans. Networking, 10(3):320–328, June 2002.
J. Mo and J. Walrand.
Fair end-to-end window-based congestion control.
IEEE/ACM Trans. Networking, 8(5):556–567, October 2000.
David Hayes david.hayes@ieee.org
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