Darbe bus nagrinėjama mišraus tipo masinė aptarnavimo sistema, kurią gali sudaryti n paraiškų šaltinių, su atitinkamais paprasčiausių srautų intensyvumais, o paraiškos gali būti paskirstomos į m aptarnavimo įrenginių su fiksuotomis prioritetinėmis paraiškų eilėmis, kur paraiškos aptarnavimo laikas S yra pasiskirstęs pagal apibendrintą tikimybinio skirstinio funkciją G(t). Darbo tikslas – sukurti programinę įrangą, kuri pagal pateiktą sistemos funkcionavimo aprašymą schematine struktūra apskaičiuoja sistemos stacionariąsias tikimybes ir tikimybines charakteristikas. / This paper analyses the underlying multi-server and multi-class queuing system which is receiving applications of corresponding intensities distributed by Poisson process and can be spread among multi-class servers with fixed waiting positions, where service time S of a application has a general probability distribution function G(t). The object of this paper is to create the software which enables to compute stationary probabilities and to estimate stochastic characteristics of the system which is defined in schematic structure.

Šiame darbe nagrinėta tam tikra asimptotiškai homogeninė Markovo grandinė ir rasta jos stacionaraus skirstinio uodegos asimptotika. Nagrinėta grandinė negali būti ištirta šiuo metu žinomais metodais, todėl darbas turi praktinę reikšmę. Spręstas uždavinys aktualus sunkių uodegų analizėje. / In this work we have investigated some asymptotically homogeneous Markov chain and found asymptotics of the stationary distribution tail. To our best knowledge, considered chain cannot be investigated by means of existing methods, hence obtained results have practical value. Solved problem is relevant in heavy tail analysis.

The research object is probabilistic properties of non-coding DNA (nucleotide) sequences. Available models of DNA sequences are reviewed and their basic assumptions are verified by statistical analysis of bacterial DNA sequences. On the ground of this analysis, the definition of non-informative genetic sequence is introduced and a mathematical model of “genetic noise” is proposed. Computer simulations of non-coding (non-informative) nucleotide sequence evolution are performed and resulting sequences are compared with native ones. The task of visualisation of genetic sequences is an important part of the work. The main tasks of the work are the following: 1. to analyse the statistical features (independence, Markovity, long-range dependence, etc.) of bacterial DNA sequences, especially non-coding ones, 2. to formulate a definition of a non-informative nucleotide sequence (“genetic noise”) and to propose its mathematical model, 3. using the methodology of functional data analysis and the distance metrics between oligonucleotides, to propose an efficient method for nucleotide sequence visualisation. General Conclusions: 1. The probability model of non-informative nucleotide sequence or, in other words, “genetic noise” (an analogue of the “white noise”) is proposed and its properties are studied mainly by computer simulation. The long-range dependence in DNA sequences has been extensively studied and is considered as an evidence of their complexity and hierarchical structure... [to full text]

The research object is probabilistic properties of non-coding DNA (nucleotide) sequences. Available models of DNA sequences are reviewed and their basic assumptions are verified by statistical analysis of bacterial DNA sequences. On the ground of this analysis, the definition of non-informative genetic sequence is introduced and a mathematical model of “genetic noise” is proposed. Computer simulations of non-coding (non-informative) nucleotide sequence evolution are performed and resulting sequences are compared with native ones. The task of visualisation of genetic sequences is an important part of the work. The main tasks of the work are the following: 1. to analyse the statistical features (independence, Markovity, long-range dependence, etc.) of bacterial DNA sequences, especially non-coding ones, 2. to formulate a definition of a non-informative nucleotide sequence (“genetic noise”) and to propose its mathematical model, 3. using the methodology of functional data analysis and the distance metrics between oligonucleotides, to propose an efficient method for nucleotide sequence visualisation. General Conclusions: 1. The probability model of non-informative nucleotide sequence or, in other words, “genetic noise” (an analogue of the “white noise”) is proposed and its properties are studied mainly by computer simulation. The long-range dependence in DNA sequences has been extensively studied and is considered as an evidence of their complexity and hierarchical structure... [to full text]