Copyright © 2007 Elsevier Ltd All rights reserved.
Throughputs in processor sharing models for integrated stream and elastic traffic
Received 10 December 2003;
Abstract
We present an analytical study of throughput measures in processor sharing queuing systems with randomly varying service rates, modelling e.g. a communication link in an integrated services network carrying prioritised fixed rate stream traffic and rate-adaptive elastic traffic. A number of distinct throughput measures for the elastic traffic are defined, analysed and compared under various system conditions, both by analytical means and simulation. It is concluded that the call-average throughput, which is most relevant from the user point of view but typically hard to analyse, is very well approximated by the newly proposed so-called expected instantaneous throughput, which is readily obtained from the system’s steady state distribution.
Keywords: Throughput; Processor sharing; Random environment
Article Outline
- 1. Introduction
- 2. Models and measures
- 2.1. Call characteristics
- 2.2. Performance models
- 2.3. Throughput measures
- 3. Performance analysis
- 3.1. Analysis of sv model
- 3.1.1. Call-average throughput
- 3.1.2. Time-average throughput
- 3.1.3. Expected instantaneous throughput
- 3.1.4. Ratio throughput measure
- 3.1.5. Comparison of throughput measures
- 3.2. Analysis of v model
- 3.3. Analysis of sd model
- 3.3.1. Call-average throughput
- 3.3.2. Time-average throughput
- 3.3.3. Expected instantaneous throughput
- 3.3.4. Ratio throughput measure
- 3.3.5. Call-average stretch
- 3.3.6. Comparison of measures
- 3.4. Analysis of d model
- 3.4.1. Call-average throughput
- 3.4.2. Time-average throughput
- 3.4.3. Expected instantaneous throughput
- 3.4.4. Ratio throughput measure
- 3.4.5. Call-average stretch
- 3.4.6. Comparison of measures
- 4. Numerical experiments
- 4.1. Parameter settings
- 4.2. Conditional throughput performance
- 4.3. Unconditional throughput performance
- 4.4. Coefficient of variation of the throughput
- 5. Concluding remarks
- Acknowledgements
- Appendix A. Proof of Theorem 1
- Appendix B. Proof of Theorem 2
- Appendix C. Proof of Theorem 3
- Appendix D. Proof of Corollary 1
- References






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