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Analysis of the Polling models with semi-Markovian delays


Author: Bejenari Diana
Degree:doctor of physics and mathematics
Speciality: 01.01.09 - Mathematical cybernetics and operation research
Year:2012
Scientific advisers: Gheorghe Mişcoi
doctor habilitat, professor, Institute of Mathematics and Computer Science of the ASM

,
Institution: Moldova State University
Scientific council: DH 30-01.01.09-27.03.08
Moldova State University

Status

The thesis was presented on the 14 September, 2012
Approved by NCAA on the 15 November, 2012

Abstract

Adobe PDF document – 0.67 Mb / in romanian

Keywords

Polling models with semi-Markovian delays, generalized priority queueing models, k-busy period, matrix method, Laplace-Stieltjes transform

Summary

Thesis structure: The thesis is written in Romanian and consists of an introduction, three chapters, conclusion, bibliography of 79 titles and an annexe. The main text of the thesis comprises 108 pages. The basic results of the thesis are published in 17 scientific papers.

Field of study of the thesis: Queueing theory. The aim of research: Elaboration of matrix methods and numerical algorithms to determine the distribution of k-busy period for Polling models with semi-Markovian delays and for generalized priority queueing models.

Scientific novelty and originality: Matrix methods to determine the distribution of k-busy period for Polling models with semi-Markovian delays and for priority queueing models were argued; the basic properties of PH distribution were formulated and demonstrated; the matrix algorithms to determine the distribution of k-busy period for studied queueing models have been elaborated and theoretical argued.

The important scientific solved problem: development of the matrix method and algorithms for solving the generalized Kendall functional equation to determine the distribution of k-busy period for Polling models with semi-Markovian delays and for generalized priority queueing models.

The theoretical significance: The results presented in the thesis can serve as scientific support for further research in studying and determining the main probabilistic characteristics of different types of queuing models.

Applicative value of the thesis: The obtained results can be applied in telecommunication systems, in transport systems, which can be modeled mathematically by the models studied in this thesis.

The implementation of the scientific results: The elaborated algorithms have been implemented as a software program using C++.