Queueing Theory 2. Nikolaos Limnios

7.2. Preliminaries 7.3. The single-server system 7.4. The zero-delayed multiserver system 7.5. The delayed multiserver system: finiteness of the first regeneration period 7.6. Instability 7.7. Related research 7.8. Acknowledgments 7.9. References

      12  8 Transient Analysis of Markovian Queueing Systems: a Survey with Focus on Closed-forms and Uniformization 8.1. Introduction 8.2. Basics on Markovian queues 8.3. First examples 8.4. An uniformization-based path for the M/M/1 with matrix generating functions 8.5. An uniformization-based path using duality 8.6. Other transient results 8.7. Conclusion 8.8. References

      13  List of Authors

      14  Index

      15  End User License Agreement

       List of Illustrations

      1 Chapter 1Figure 1.1. A road intersected by a pedestrian crossingFigure 1.2. Plots for α = 0.5, 1.5, 2

      2 Chapter 2Figure 2.1. One-lag correlation coefficient of MAPs under different scenarios. F...Figure 2.2. Selected measures for a MAP/PH/1 queue under different scenariosFigure 2.3. Tail probabilities for the sojourn time for a MAP/PH/1 queue under d...Figure 2.4. The distribution function of the sojourn time for a MAP/PH/1 queue u...Figure 2.5. Selected measures for a MAP/M/c queue under different scenariosFigure 2.6. Ratio of the mean busy period to the mean sojourn time for (simulate...Figure 2.7. Ratio of the mean queue length for MAP/PH/1 vacation to MAP/PH/1 cla...Figure 2.8. Ratio of the system idle probability for vacation and classical MAP/...Figure 2.9. The distribution functions of the sojourn time for MAP/PH/1 classica...Figure 2.10. The distribution functions of the sojourn time for MAP/PH/1 classic...Figure 2.11. Selected measures for (simulated) a BMAP/PH/c queue with a vacation...Figure 2.12. The tail probabilities of the sojourn time for (simulated) a BMAP/G...

      3 Chapter 5Figure 5.1. The GE-type distribution with parametersFigure 5.2.

versus n for

versus n for

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versus n for | For a color version of this figure, see www.iste.co...Figure 5.5.

versus n for | For a color version of this figure, see www.iste.co...Figure 5.6.

versus n for

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and

versus n for q for original | For a color version of this fi...Figure 5.8.

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versus q for original

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and

versus q for original

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      4 Chapter 8Figure 8.1. The evolution of an individual particle in the continuous-time Ehren...Figure 8.2. An example where a closed-form for the transient behavior is easy to...Figure 8.3. Uniformization of the M/M/1 canonical process w.r.t. the uniformizat...Figure 8.4. The Siegmund-dual of the standard birth-death process with birth rat...Figure 8.5. This is a pair (X, X*) where the dual exists under specific conditio...Figure 8.6. Process X has no dual, whatever the value of λ (and, obviously, what...Figure 8.7. The dual Z^* of the uniformization Z of the M/M/1 process, which is a...Figure 8.8. The M/M/1/H model, parameters λ and μFigure 8.9. The uniformized chain of the M/M/l/H canonical process depicted in

Figure 8.10. The dual process of the M/M/1/H given in Figure 8.8Figure 8.11. The dual of the uniformized chain shown in Figure 8.9, which is als...Figure 8.12. The smallest non-trivial irreducible Markov process with two states...Figure 8.13. The M/M/1/H model with catastrophes; parameters: arrival rate λ, se...Figure 8.14. The dual of the M/M/1/H model with catastrophes is depicted in Figu...Figure 8.15. The uniformization of the dual of the M/M/1/H model with catastroph...Figure 8.16. Auxiliary 2-dimensional process YFigure 8.17. The uniformization of process Y depicted in Figure 8.16 with respec...Figure 8.18. A numerical example where λ = 0.95 and μ = 1; we plot

, for level ...

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