Optimal Load-Balancing

1
Optimal Load-Balancing

• Isaac Keslassy (Technion, Israel),
• Cheng-Shang Chang (National Tsing Hua University,
  Taiwan),
• Nick McKeown (Stanford University, U.S.A.),
• Duan-Shin Lee (National Tsing Hua University,
  Taiwan)

2
Router Designer Wishlist

• Mesh Switch avoid switch reconfiguration and
  complex scheduling algorithms. Practical for
  optics (AWGR).
• 100 Throughput router guaranteed to be stable
  under any admissible traffic matrix
• Minimum Linecard Complexity? Minimize maximum
  rate at which packets arrive to/depart from any
  input/output.
• Buffering Speed
• Processing Speed

3
Naive Mesh with 100 Throughput
R
In
R
In
In
4
Output-Queued Mesh
?

• Mesh
• 100 throughput
• but output write speed NR

?
5
If Traffic Is Uniform
R
In
R
In
R
In
6
100 Throughput Non-Uniform Traffic Matrices
7
Load-Balanced Router
R
R
R
R/N
Out
R/N
In
R/N
R/N
R/N
R/N
R/N
R/N
R
R
R
In
R/N
R/N
R/N
R/N
R/N
R/N
R
R
R
R/N
R/N
In
R/N
R/N
Load-balancing mesh
Forwarding mesh
Theorem 100 Throughput Val. 82, CLJ 01, K. et
al. 03
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Load-Balanced Router
R
R
In
R/N
R/N
1
2
3
R/N
R/N
R/N
R/N
R/N
R/N
R
R
In
R/N
R/N
R/N
R/N
R/N
R/N
R/N
R
R
R/N
In
R/N
R/N
9
Load-Balanced Router
R
R
In
R/N
R/N
R/N
R/N
1
R/N
R/N
R/N
R/N
R
R
In
R/N
R/N
2
R/N
R/N
R/N
R/N
R/N
R
R
R/N
In
R/N
R/N
3
10
Load-Balanced Router
?

1. Mesh ? 2 meshes
2. 100 throughput
3. Node speed?

?
?
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Combining the Two Meshes
R
In
R/N
R/N
R/N
R/N
R
In
R/N
R/N
R/N
R
R/N
In
R/N
12
A Single Combined Mesh
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Matrix for the Combined Mesh

• Combined mesh matrix
• The combined mesh matrix gets 100 throughput

14
Node Speed for Combined Mesh

• Max input/output read/write speed 2R

15
Combined Mesh
?

1. Single Mesh
2. 100 Throughput
3. Max Node Speed 2R

?
?
Question is 2R optimal? Any better architecture?
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Can Another Architecture Do Better?

• Criteria Given all architectures with 100
  throughput, minimize the maximum node processing
  speed.

17
Other Mesh Architectures We Consider

• Any number of stages (e.g., 3 stages, 4 stages.)
• Any mesh architecture (e.g., ring)
• Any link capacities (e.g., non-uniform mesh)
• Any packet routing algorithm (e.g., adaptive
  algorithm)

Any mesh and any routing.
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Example 1 Add A Third Mesh?
1st stage
2nd stage
3rd stage
Combine the 3 meshes ? Max speed 3R (instead
of 2R)
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Example 2 Use a Non-Uniform Mesh

• This is actually a ring!

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Example 2 Unidirectional Ring

• Assume that each node sends all traffic to
  itself.
• Then each packet goes through N nodes.
• To get 100 throughput, each node needs to run N
  times faster.

? Max speed NR (instead of 2R)
21
At First Glance

• it seems that the uniform mesh is optimal with
  2R!
• Why
• All links have the same capacity,
• And it is perfectly symmetric.
• However. uniform mesh is NOT optimal!

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Why Uniform Mesh is Not Optimal

• Links between two different nodes used for
  spreading and forwarding
• Same-node links only used for forwarding, not
  spreading ? need less capacity.
• Example packet from node 1 to node 2. No point
  in sending it from node 1 to node 1 before
  forwarding to node 2!

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Main Result
Slightly Non-Uniform Mesh
Slightly better than 2R
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However

• The result is actually good for the load-balanced
  router with uniform mesh.
• The uniform mesh is optimal as N ? 1
• In other words, asymptotically with N, the
  load-balanced router is at least as good as any
  other mesh architecture with any other routing
  algorithm.

The load-balanced router satisfies the wishlist
goals.
25
Generalization Load-Balanced Network

• Hotnets III, Nov. 2004
• Zhang-Shen and McKeown
• Kodialam, Lakshman and Sengupta
• Two steps
• Uniform spreading of incoming packets
  (independently of destination)
• Forwarding to destination

2
1
2
0
1
3
N

• A uniform load-balanced backbone
• guarantees 100 throughput for any traffic matrix
  
• is at least as good as any other backbone design

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Thank you.