National Repository of Grey Literature 14 records found  previous11 - 14  jump to record: Search took 0.01 seconds. 
Models of Queueing Systems
Horký, Miroslav ; Dvořák, Jiří (referee) ; Šeda, Miloš (advisor)
The master’s thesis solves models of queueing systems, which use the property of Markov chains. The queueing system is a system, where the objects enter into this system in random moments and require the service. This thesis solves specifically such models of queueing systems, in which the intervals between the objects incomings and service time have exponential distribution. In the theoretical part of the master’s thesis I deal with the topics stochastic process, queueing theory, classification of models and description of the models having Markovian property. In the practical part I describe realization and function of the program, which solves simulation of chosen model M/M/m. At the end I compare results which were calculated in analytic way and by simulation of the model M/M/m.
Queueing theory utilization in packet network design and optimization process
Rýzner, Zdeněk ; Zeman, Václav (referee) ; Novotný, Vít (advisor)
This master's thesis deals with queueing theory and its application in designing node models in packet-switched network. There are described general principles of designing queueing theory models and its mathematical background. Further simulator of packet delay in network was created. This application implements two described models - M/M/1 and M/G/1. Application can be used for simulating network nodes and obtaining basic network characteristics like packet delay or packet loss. Next, lab exercise was created, in that exercise students familiarize themselves with basic concepts of queueing theory and examine both analytical and simulation approach to solving queueing systems.
Non-negative linear operators and their use in econometric and statistic models
Horský, Richard ; Arlt, Josef (advisor) ; Vrabec, Michal (referee) ; Klazar, Martin (referee)
Non-negative operators, in special case non-negative matrices, are an interesting topics for many scientists and scientific teams from the beginning of the 20th century. It is not suprising because there are a lot of applications in different areas of science like economy, statistics, linear programming, computer science and others. We can give as the particular example the theory of the Markov chains in which we deal with non-negative matrices, so called transition matrices. They are of the special form and we called them stochastic matrices. Another example is given by the non-negative operator on spaces of infinite dimension which is employed in the theory of stochastic processes. It is the backward shift operator called the lag operator as well. The non-negativity in these examples is considered as the piecewise non-negativity. Another type of non-negativity is that in the sense of inner products. In the case of matrices we talk about positive-definite or positive-semidefinite matrices. A typical example is the covariance matrix of a random vector or symmetrization of any linear operator, for instance the symmetrization of the difference operator. The terms inverse problem or ill-posed problem have been gaining popularity in modern science since the middle of the last century. The subjects of the first publications in this area were related to quantum scattering theory, geophysics, astronomy and others. Thanks to powerful computers the chances for applications of the theory of inverse and ill-posed problems has extended in almost all fields of science which use mathematical methods. Ill-posed problems bear the feature of instability and there is the need of regularization if we want to get some reasonable solution. A typical example of the regularization is the differencing of stochastic process with the purpose to obtain a stationary process. Another concept of regularization used for solving e.g. integral equations with compact operators consists in application of regularization method as truncated singular value decomposition, Tichonov regularization method or Landweber iteration method. Mathematical tools employed in this work are those of the functional analysis. It is the area of mathematics in which distinct mathematical structures meet each other. They are structures built within different mathematical disciplines as mathematical analysis, topology, theory of sets, algebra (mainly linear algebra) and theory of measure (probability). The functional analysis framework enables us to obtain right formulations of definitions and problems providing the general view on the notions and problems of the theory of stochastic processes.
Capital protected funds
Houdek, Ondřej ; Witzany, Jiří (advisor) ; Prokop, Martin (referee)
This thesis is mainly focused on pricing securities of selected capital protected funds. In its theoretical part, there are summarized approaches and principals that are generally used for derivatives pricing because capital protected funds' securities contain embedded options. Emphasis is put on risk-neutral pricing using Monte Carlo simulation at that point because complicated pay-off functions of these funds are hard to be evaluated analytically. There are also presented main approaches to constructions and portfolio management of these funds from their portfolio manager's viewpoint. Finally, there is made an overview of basic types of capital protected funds issued both in The Czech republic and Europe. Analytical part is focused on evaluation of selected capital protected funds. There is applied a standard approach that is based on a simulation of Geometric Brownian Motion with constant conditional variance and correlation in contrast with an advanced approach where the conditional variance and conditional correlation matrix are simulated as well. That is accomplished with GARCH-in-mean and DCC-GARCH models. Estimated prices are compared with real market prices and there is also performance of the standard models compared with performance of advanced ones.

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