StatusThe thesis was presented on the 16 October, 2007
Approved by NCAA on the 20 December, 2007
Abstract– 0.23 Mb / in romanian
1.19 Mb /
The thesis is devoted to the study of priority queueing systems with random switchover times. It is developed the classification for the reach class of queueing systems with one server which switches between waiting lines of requests distinguished by their importance, and thus prioritised.
We recapitulate the analytic results for such systems under the assumption of Poisson incoming flows and special structure of switchover times. These results are formulated by means of systems of functional recurrent equations stated in terms of Laplace transforms of the characteristics of interest. These results are thoroughly analysed. The functional Kendall equation makes an important part of them.
It is mentioned that the case of switchover times of general structure was not studied in the literature. Yet, even for the systems Mr |Gr| 1 , generally, it is impossible to obtain the solutions to the theoretical results in analytic form.
Therefore, it is suggested to treat such kind of results numerically. For this purpose the Kendall equation is studied by exploring the introduced Kendall functional operator. The classical iterative algorithm of numerical solution of the Kendall equation is improved in such a way that it can be efficiently used in solving mentioned systems of functional recurrent equations. The accelerations schemes (Salzer summation and Wynn's Rho algorithm) for the Laplace transform’s inversion method based on Gaver functionals are used to invert the solutions and obtain complete information on the system performance characteristics. The methodology is developed for the busy periods of the systems under study. This allows one to study many other characteristics of the system, in particular, the workload coefficient ρ.
The method of imitational modelling is applied to the study of priority systems with switchover times of general structure. The Java package PQSST was developed and it allows one to imitate such systems and to obtain full empirical information on the system performance characteristics, particularly on the busy periods, idle periods, mean waiting times, loss probabilities. The detailed chronology of the processes which take place in priority system is provided by the package PQSST.
The comparative analysis of the solutions obtained by using these two different
approaches – numerical and imitational modelling methods – is carried out. The
paper is accompanied with illustrative examples. There are also discussed
applications of priority queueing systems with switchover times in traffic network