Router Level Flow Control in Data Networks

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Router Level Flow Control in Data Networks

• Stephan Bohacek
• University of Southern California

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Outline

• introduction
• 1-hop controllers
• system description
• stability
• blocking
• 2-hop controllers
• system description
• classical design methods (intuition)
• hop over
• back pressure
• forward pressure
• time constant
• modern design methods
• LQ
• L1
• distributed parameter
• stability
• future work and conclusions

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Problem Sending a packet that will be dropped is
inefficient.
Objective To avoid transmission of packets that
will be dropped (best to drop packets at the
entry point of the network).
Method Control the router sending rates to ease
and regulate network congestion.
For very high speed networks it might be better
to use hop-by-hop flow control instead of
end-to-end flow control.
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one hop controller
Let
Queue dynamics
Link rate dynamics
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one hop controller
Router B
Router A
Router C
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stability of one hop controller
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Blocking
C
A
E
Congested router
Slow link
B
D

• The data leaving A is destined for C.
• The data leaving B is destined for D.
• Link E-D is slow, so the queue in E fills.
• Back pressure slows down both links A-E and B-E.
• However, the link from E-C is high speed, hence
  the link A-E is slowed needlessly.

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two hop controller
C
B
A
D
(queues in B are empty)
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two hop controller
Queue Dynamics
Rate Controller
How to set control parameters?
intuition vs. optimization
classical vs. modern
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Forward Pressure
Back Pressure
Congested Router
Data
Control
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As queue fills, out going data rates rapidly
increase
As queue fills, out going data rates slowly
increase
That is, the router sends data at the maximum
rate whenever the queue is not empty.
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A
B
C
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A
B
C
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Back Pressure
C
A
B
D

• If queue C-D fills
• Rate B-C slows
• Queue B-C fills
• Rate A-C slows
• Queue A-C fills

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Back Pressure
constant input
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Back Pressure
input
constant input
input
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Without Back Pressure
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With Back Pressure
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Forward Pressure
Forward Pressure
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Forward Pressure
1. input data
3. data flows
5. data flows rapidly - queue B-C is filling -
queue A-C is filling
2. queue fills
4. queue fills
A
B
C
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Without forward pressure
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With forward pressure
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Blocking
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Blocking
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Blocking
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Blocking
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modern control methods(with truncation)

• optimal control with quadratic cost
• minimize peak queue/rate size
• distributed parameter

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linear quadratic
Quadratic Cost
Let
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Show plot of gains
Note gains decay, hence truncation LQ doesnt
make much use of back pressure lack of back
pressure can be seen by the small gains from
26-27, 26-19 and 26-33
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L1 Control methods
Minimize peak queue size
Objective
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L1 Control methods
subject to
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Note on previous slide, good back pressure, some
forward pressure. But no back pressure from 8-5.
Why? These optimization procedures dont always
give intuitive answers. Is it that the
optimization procedure is better, or doing
something stupid.
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Distributed Parameter Methods
Simple 1-D spatially invariant system
I/O
Data Flow
Control Information
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Distributed Parameter Methods
Temporal Dynamics (only depends on local
variables)
Spatial dynamics
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Distributed Parameter Methods
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Distributed Parameter Methods
- Compact description of large system -
Controllers will depend on local variables only
advantages
Requires systems be homogeneous. Extending it to
nonhomogeneous systems may lead to computational
difficulties.
disadvantages -
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stability
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Note that there still are some slow
eigenvalues. These are from alphas that result in
data taking a long time to get out of the
network. That is, nonsensical alphas. It seems
that making reasonable alphas is difficult
The previous network is 3 x 3, with K4 and K6 0
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1
4
2
3
Has a pole at zero, integrator
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1
4
Take the sum of possible input-output
pairs. These sums lead to sensible
2
3
1
4
2
3
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stability
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Future Directions

• characterization of alphas
• simulation with TCP and CBR data
• rigorous controller synthesis
• rigorous stability and performance analysis
• investigation of differences between TCP and CBR
  traffic in such a network