Network Information Flow in Network of Queues

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Network Information Flow in Network of Queues
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• Phillipa Gill, Zongpeng Li,
• Anirban Mahanti, Jingxiang Luo,
• and Carey Williamson
• Department of Computer Science
• University of Calgary

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1
Now at University of Toronto. Now at IIT Delhi,
India.
IEEE/ACM MASCOTS 2008
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The Story Network Modeling

• Queueing networks
• Well-established modeling methodology
• Network information flow
• Another well-established approach
• These two different approaches have different
  strengths and weaknesses
• Q Can we blend the two together?
• A We think so.

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Queueing Networks (1 of 3)

• Single Queue

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M/M/1 q / (1 ) where /

Literature ACM SIGMETRICS, IFIP Performance,
IEEE/ACM MASCOTS, Performance
Evaluation, Queueing Systems,
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Queueing Networks (2 of 3)

• Chain of Queues

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Queueing Networks (3 of 3)

• Networks of Queues

...
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Queueing Networks Summary

• Good
• Models finite node capacity (rate, storage)
• Realistic models of stochastic traffic
• Realistic models of nodal delay and loss
• Bad
• Naïve and unrealistic network topology
• Ignores multi-hop flow routing concept
• Hop-by-hop (atomic) view, not end-to-end

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Network Flow (1 of 3)

• Maximize unicast flow from S to T

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B
A
Capacity
Cost
10
8
3
5
9
3
5
S
T
4
10
3
6
5
10
5
8
5
C
D
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Literature IEEE INFOCOM, CORS/ORSA, STOC,
IEEE JSAC, Trans. on Information
Theory,
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Network Flow (2 of 3)

• Minimize cost of unit flow from S to T

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B
A
Capacity
Cost
10
8
3
5
9
3
5
S
T
4
10
3
6
5
10
5
8
5
C
D
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Network Flow (3 of 3)

• Multicast flow from S to R1, R2, and R3

Multicast approach has server cost 3, network
cost 6
Assumptions - Multicast flow has unit
capacity (i.e., 1). - All edges have the same
unit capacity, and the same cost. -
Information flows are replicable and encodable.
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Network Flow (3 of 3)

• Multicast flow from S to R1, R2, and R3

Better approach has server cost 2, network cost 5
Assumptions - Multicast flow has unit
capacity (i.e., 1). - All edges have the same
unit capacity, and the same cost. -
Information flows are replicable and encodable.
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Network Flow (3 of 3)

• Multicast flow from S to R1, R2, and R3

Network coding approach has server cost
1.5, network cost 4.5
Assumptions - Multicast flow has unit
capacity (i.e., 1). - All edges have the same
unit capacity, and the same cost. -
Information flows are replicable and encodable.
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Network Flow Summary

• Good
• Properly reflects network topology
• Captures the multi-hop flow routing aspect
• Can exploit benefits of network coding
• Bad
• Implicitly assumes nodes are very powerful
• Ignores nodal processing delay
• Ignores queueing delay and loss

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Research Questions

• Can we combine the two approaches, so that we
  get the best of both worlds?
• Non-trivial network topologies
• Multi-hop routing
• Stochastic traffic
• Nodal processing, queuing delay, loss...
• Does such an approach lead to new, interesting,
  and different insights, compared to classic
  network information flow or queueing network
  models?

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Methodology

• Mathematical modeling as a convex optimization
  problem (optimal routing)
• Deterministic, non-trivial multi-hop flows
• Stochastic traffic, nodal queueing delays
• For each routing scenario
• Construct the mathematical program
• Prove that objective function and the feasibility
  region are convex (solvable)
• Perform simulation for numerical results

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Example Single Unicast
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• Minimize
• Subject to

Weighted Delay (cost)
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f (u) (u)
in
?
u V
Queueing Delay
u
Stability
u
Target Volume
Flow Conservation
Capacity Constraint
Non-negative values
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Evaluation Methodology

• Network topology generation BRITE
• Convex optimization MATLAB and cvx
• Numerical results interpreted
• Model correctness verified
• Results with the new model can behave differently
  than (for example) network models based on
  (linear) link costs

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Example Numerical Results
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Modeling Issues

• Analysis of queueing network models often relies
  on memoryless property (i.e., Poisson arrivals
  and departures)
• Network coding implies some sort of
  synchronization between two streams
• Q Is our approach doomed?
• A No. Poisson property is preserved! (see
  proof in paper via Markov chains)

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Summary and Conclusions

• We proposed a new approach to network modeling,
  which combines classic network information flow
  with queueing networks
• Preliminary results with this model look very
  promising
• Memoryless property preserved
• New insights on optimal routing
• Ending of the story is yet to be written!