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On Performance Bounds for the Integration of Elastic and Adaptive Streaming Flows
Thomas Bonald, Alexandre Proutière
To cite this version:
Thomas Bonald, Alexandre Proutière. On Performance Bounds for the Integration of Elastic and Adaptive Streaming Flows. ACM Sigmetrics, 2004, New York, United States. �hal-01282906�
On Performance Bounds for the Integration of Elastic and Adaptive Streaming Flows
Thomas Bonald and Alexandre Prouti `ere
France Telecom R&D
38-40 rue du G ´en ´eral Leclerc, 92794 Issy-les-Moulineaux, France
ABSTRACT
Categories and Subject Descriptors
General Terms
Keywords
1. INTRODUCTION
SIGMETRICS/Performance’04,June 12–16, 2004, New York, NY, USA.
.
2. A SINGLE BOTTLENECK LINK
2.1 Traffic assumptions
2.2 Performance metrics
2.3 A processor sharing network
Absence of streaming traffic.
Presence of streaming traffic.
2.4 Insensitive bounds
Upper bound.
Lower bound.
All traffic elastic.
2.5 Numerical example
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Elatsic flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Streaming flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
3. ACCOUNTING FOR RATE LIMITS
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Pr[ streaming throughput > 0.1 ]
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
3.1 Traffic assumptions
3.2 A processor sharing network
3.3 Insensitive bounds
Upper bound.
Lower bound.
All traffic elastic.
3.4 Numerical example
4. MULTICLASS EXTENSION
0 0.02 0.04 0.06 0.08 0.1
0 0.2 0.4 0.6 0.8 1
Elastic flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.02 0.04 0.06 0.08 0.1
0 0.2 0.4 0.6 0.8 1
Streaming flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
Notation.
4.1 Balanced fairness
4.2 Traffic assumptions
4.3 A processor sharing network
4.4 Insensitive bounds
Upper bound.
Lower bound.
All traffic elastic.
4.5 Numerical examples Tree network.
C1 C2
1
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Elastic flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Streaming flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.1 0.2 0.3 0.4 0.5
0 0.2 0.4 0.6 0.8 1
Elastic flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.1 0.2 0.3 0.4 0.5
0 0.2 0.4 0.6 0.8 1
Streaming flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
Multirate system.
a1
a2
1
0 0.1 0.2 0.3 0.4 0.5
0 0.2 0.4 0.6 0.8 1
Elastic flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.1 0.2 0.3 0.4 0.5
0 0.2 0.4 0.6 0.8 1
Streaming flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.05 0.1 0.15 0.2 0.25
0 0.2 0.4 0.6 0.8 1
Elastic flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
0 0.05 0.1 0.15 0.2 0.25
0 0.2 0.4 0.6 0.8 1
Streaming flow throughput
Elastic traffic load Upper bound
Simulation Lower bound All traffic elastic
5. CONCLUSION
APPENDIX
A. INSENSITIVITY RESULTS
Balanced networks.
x x
1 2
φ φ
0
x
1 2
Non-balanced networks.
B. PROOF OF THEOREM 1 Necessary stability condition.
Sufficient stability condition.
C. PROOF OF PROPOSITION 1 Proof of inequality (20).
Proof of inequality (21).
REFERENCES
