Transcript Providing 100% throughput for non-uniform Bernoulli traffic Shang-Tse (Da) Chuang Siva Gaggara Motivation • Maximum Weight Matching can provide 100% throughput with a speedup of.

Providing 100% throughput for
non-uniform Bernoulli traffic
Shang-Tse (Da) Chuang
Siva Gaggara
Motivation
• Maximum Weight Matching can provide 100%
throughput with a speedup of 1. (McKeown)
(Dai,Prabhakar)
• Any maximal matching algorithm can provide 100%
throughput with a speedup of 2. (Dai,Prabhakar)
• What speedup is required to provide 100%
throughput using a practical maximal matching
algorithm?
Problem Statement
S=1
Find λmax
•non-uniform Bernoulli traffic with rate λij
•Σi λij < λmax and Σj λij < λmax
•FPWWFA is the maximal matching algorithm
Wrapped Wave Front Arbiter
(Tamir) reminder
1
2
3
1
2
Friends, Strangers, Enemies
1
2
3
λ11 λ12 λ13
1
λ21 λ22 λ23
2
λ31 λ32 λ33
• Flows λ11,λ21,λ32, and λ33 are enemies
• Flows λ12,λ13, and λ22 are strangers
• Flow λ23 is a friend
The “L” Traffic Pattern
1
2
3
λ11 0
0
1
λ21 0
0
2
(1-λ11)
λ21
λ31 λ32 λ33
• Q31

 21 
service rate = 1   32   331  111 

1  11 

= 1   32   331  11   21
•Thus, for this traffic pattern, λmax = 0.75
Throughput Formula
1
2
3
λ11 0
0
1
λ21 0
λ23
2
(1-λ11)(1-λ23)
λ21
(1-λ23)(1-λ32)
λ33
λ31 λ32 λ33
• Q31 service rate = 1  111   32  23 
1  111   32 1   231 

 21


 33
1 

1  111   23  1   32 1   23 
•Greater than L-traffic analysis for all λ23
Simulation
λ11 = 0.2, λ21 = 0.3, λ32 = 0.15, λ33 = 0.35
Conclusions
• λmax = 0.75 for “L” traffic pattern
• Found throughput formula that matches simulation
for any non-uniform Bernoulli traffic pattern for a
3x3 switch
• We believe that λmax = 0.75 is true for any nonuniform Bernoulli traffic pattern for any switch
size