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Performance Evaluation
Volume 65, Issues 6-7, June 2008, Pages 484-511
Innovative Performance Evaluation Methodologies and Tools: Selected Papers from ValueTools 2006
 
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doi:10.1016/j.peva.2007.12.008    
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Copyright © 2008 Elsevier Ltd All rights reserved.

Controlling the delay trade-off between packet flows using multiple reserved places

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S. De VuystCorresponding Author Contact Information, a, E-mail The Corresponding Author, S. Wittevrongela, D. Fiemsa and H. Bruneela

aSMACS Research Group, Department of Telecommunications and Information Processing, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium 1


Received 30 October 2007; 
revised 7 December 2007; 
accepted 17 December 2007. 
Available online 6 January 2008.

Abstract

We analyse a discrete-time queueing model with packet arrivals that are either delay-sensitive (type 1) or delay-tolerant (type 2). The prominent feature of this model is its reservation-based queueing discipline, which reduces the queueing delay perceived by the 1-packets at the cost of allowing higher delays for the 2-packets. A total of N reserved places are introduced in the queue. Whenever a 1-packet enters the queue, it takes the position of the most advanced reservation and creates a new one at the end of the queue. The amount of delay differentiation between 1- and 2-packets can thus be controlled smoothly by the parameter N. We obtain the probability-generating function, the mean value and the tail distribution of the delay experienced by 1- and 2-packets.

Keywords: Discrete-time queueing model; Priority; Place reservation; Queueing discipline; Delay analysis

Article Outline

1. Introduction
2. Mathematical model and system equations
3. Equilibrium distribution of the system state
4. Two basic theorems
5. Delay of type 1 packets
5.1. The pgf D1(z) of the type 1 packet delay
5.2. Distribution of the first reservation position
5.3. A double transform
5.4. Mean value of the type 1 packet delay
5.5. Tail distribution of the type 1 packet delay
6. Delay of type 2 packets
6.1. Content of the virtual View the MathML source-queue: A PH-type distribution
6.2. The pgf D2(z) of the type 2 packet delay
6.3. Matrices of finite dimension only
6.4. Spectral decomposition of View the MathML source
6.5. Mean value of the type 2 packet delay
6.6. Tail distribution of the type 2 packet delay
7. Discussion of results: Some examples
8. Conclusion
Acknowledgements
References
Vitae










Corresponding Author Contact InformationCorresponding author. Tel.: +32 9 2648902; fax: +32 9 2644295.
1 SMACS: Stochastic Modeling and Analysis of Communication Systems.

Performance Evaluation
Volume 65, Issues 6-7, June 2008, Pages 484-511
Innovative Performance Evaluation Methodologies and Tools: Selected Papers from ValueTools 2006
 
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