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Performance Evaluation
Volume 65, Issue 2, February 2008, Pages 152-180
 
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doi:10.1016/j.peva.2007.05.002    
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Copyright © 2007 Elsevier Ltd All rights reserved.

Throughputs in processor sharing models for integrated stream and elastic traffic

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Remco Litjensa, Hans van den Berga, b, Corresponding Author Contact Information, E-mail The Corresponding Author and Richard J. Boucheriec

aDepartment of Planning, Performance and Quality, TNO ICT, The Netherlands

bDepartment of Computer Science, University of Twente, The Netherlands

cDepartment of Applied Mathematics, University of Twente, The Netherlands


Received 10 December 2003; 
revised 18 January 2007; 
accepted 11 May 2007. 
Available online 17 May 2007.

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







Corresponding Author Contact InformationCorresponding author at: Department of Planning, Performance and Quality, TNO ICT, The Netherlands. Tel.: +31 152857031; fax: +31 152857349.

Performance Evaluation
Volume 65, Issue 2, February 2008, Pages 152-180
 
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