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Mykhalevych, Kyryl (2005) Sensitivity of typical queueing systems. Doctoral thesis, London Metropolitan University.
The PhD project includes analytical and numerical investigation of two different queueing models (loss systems and retrial queueing systems) having the following essential common features:
- the system is described by a generic distribution from a parametric family;
- the limiting behaviour of this distribution is considered (light-traffic, small orbit time etc.);
- the validity of some analytical formulae for queueing indexes is checked under critical values of generic parameters.
Chapter 1 presents the summary of the project and contains a review of the literature on the topic.
In Chapter 2 the limiting behaviour of steady-state loss probability PLoss in cases of "unsmoothly" behaved generic distributions is investigated. This problem was motivated by J.B. Atkinson who discovered three sources of light-traffic insensitivity by numerical analysis, and by Prof. I.N. Kovalenko who initiated the investigation of so-called light-traffic insensitivity in several papers.
In Chapter 3 with the help of numerical analysis of certain queueing systems it is shown that there is no CA2 (inter-arrival time squared coefficient of variation), for which an insensitivity of PLoss to the changes of CB2 (service time squared coefficient of variation) takes place. In addition, numerical analysis of approximate formulae for limiting cases in an H2/H21/1/ queueing system is carried out.
Chapter 4 consists in numerical analysis of a complex loss system describing the traffic of emergency stations. In particular, the accuracy of two approximate models for the loss probability, suggested by J. Ben Atkinson and I.N. Kovalenko, respectively, is checked.
Chapter 5 is devoted to the analysis and comparison of three different retrial queueing systems: cyclic-waiting system, classical retrial queueing system and retrial queueing system with dynamic service priority.
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