Copyright © 2008 Elsevier Ltd All rights reserved.
Controlling the delay trade-off between packet flows using multiple reserved places
Received 30 October 2007;
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
-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
- 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. Tel.: +32 9 2648902; fax: +32 9 2644295.1 SMACS: Stochastic Modeling and Analysis of Communication Systems.






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