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Distributed Systems Simulation
Ďuriš, Anton ; Šeda, Miloš (referee) ; Matoušek, Radomil (advisor)
This thesis is focused on distributed systems modeling using Petri nets. Distributed systems are increasingly being implemented in applications and computing systems, where their task is to ensure sufficient performance and stability for a large number of its users. When modeling a distributed systems, stochastic behavior of Petri nets is important, which will provide more realistic simulations. Therefore, this thesis focuses mainly on timed Petri nets. The theoretical part of this thesis summarizes distributed systems, their properties, types and available architectures, as well as Petri nets, their representation, types and the principle of an operation. In the practical part, two models were implemented, namely a horizontally scaled web application divided into several services with a distributed database and a large grid computing system, more precisely the BOINC platform with the Folding@home project. Both models were implemented using the PetNetSim library of Python. The goal of this thesis is to perform simulations on the created models for different scenarios of their behavior.
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Markov processes (analytic and probabilistic point of view)
Nováková, Eva ; Janák, Josef (advisor) ; Maslowski, Bohdan (referee)
This Bachelor Thesis tackles the basics of the Markov chains theory. The first four chapters describe fundamental definitions and theorems of the theory of Markov chains, both in continuous and discrete time and both with discrete and general state space. The last chapter contains examples of each type of Markov chains. The conclusion describes the relation between all four types of Markov chains.
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Distributed Systems Simulation
Ďuriš, Anton ; Šeda, Miloš (referee) ; Matoušek, Radomil (advisor)
This thesis is focused on distributed systems modeling using Petri nets. Distributed systems are increasingly being implemented in applications and computing systems, where their task is to ensure sufficient performance and stability for a large number of its users. When modeling a distributed systems, stochastic behavior of Petri nets is important, which will provide more realistic simulations. Therefore, this thesis focuses mainly on timed Petri nets. The theoretical part of this thesis summarizes distributed systems, their properties, types and available architectures, as well as Petri nets, their representation, types and the principle of an operation. In the practical part, two models were implemented, namely a horizontally scaled web application divided into several services with a distributed database and a large grid computing system, more precisely the BOINC platform with the Folding@home project. Both models were implemented using the PetNetSim library of Python. The goal of this thesis is to perform simulations on the created models for different scenarios of their behavior.
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Markov processes (analytic and probabilistic point of view)
Nováková, Eva ; Janák, Josef (advisor) ; Maslowski, Bohdan (referee)
This Bachelor Thesis tackles the basics of the Markov chains theory. The first four chapters describe fundamental definitions and theorems of the theory of Markov chains, both in continuous and discrete time and both with discrete and general state space. The last chapter contains examples of each type of Markov chains. The conclusion describes the relation between all four types of Markov chains.
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Statistická fyzika frustrovaných evolučních her
Pištěk, Miroslav ; Janiš, Václav (referee) ; Slanina, František (advisor)
1 Title: Statistical Physics of Frustrated Evolutionary Games Author: Miroslav Pištěk Department: Institute of Theoretical Physics Supervisor: RNDr. František Slanina, CSc. Supervisor's e-mail address: slanina@fzu.cz Abstract: In last two decades, the effort devoted to interdisciplinary research of bounded sources allocation is growing, examining complex phenomena as stock markets or traffic jams. The Minority Game is a multiple-agent model of inevitable frus- tration arising in such situations. It is analytically tractable using the replica method originated in statistical physics of spin glasses. We generalised the Mi- nority Game introducing heterogenous agents. This heterogeneity causes a con- siderable decrease of an average agent's frustration. For many configurations, we achieve even a positive-sum game, which is not possible in the original game variant. This result is in accordance with real stock market data. Keywords: frustrated evolutionary games, Minority Game, Replica method
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Market making jako obchodní strategie
Čamaj, Matej ; Stádník, Bohumil (advisor) ; Fičura, Milan (referee)
The purpose of this thesis is to analyze market making trading strategy and explore possibilities of using such strategy for intraday trading on the markets with the limit order book. In theoretical part we prove profitability of specified market making strategy under certain assumptions and moreover analyze effect of change of parameters on the performance of the strategy using one dimensional stochastic processes. Next the assumption of constant fair price is relaxed which leads to deterioration of profitability of these strategies. Because one dimensional stochastic processes do not capture price creation in the real world, we propose stochastic model of intraday trading in the next chapter. Advantage of this approach is that we can observe state of the limit order book during whole trading session and therefore better simulate conditions for test of the strategies. Although proposed model exhibit many phenomenons observed in empirical data like volatility clustering, in some situations it produces unrealistically high spread caused by the construction of the model, because arrivals of market and limit orders are modeled as independent processes. Another disadvantages are need of relatively extensive data for model calibration and high sensitivity of model to change of parameters. Lastly we test three different market making strategies under different choice of model parameters and show that expected profitability is positive in all cases.
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Testing hypothesis in general exponential models
Fajfrová, Lucie
The paper concerns the testing hypothesis about parameter in such families of stochastic processes that they have an exponential density with respect to a reference measure. We focus on divergence statistics, particularly so called Renyi statistics. There are examples of testing on the base of Renyi statics for some well known processes.
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Markovská vlastnost trhu s limitními objednávkami
Šmíd, Martin
We formulate a rigorousmathematical description of a limit order market (we describe the state of the market by means of atomic measures). Further, we state sufficient conditions for the evolution of the market to be Markov; in particular, all the agents should either trade randomly or use strategies dependent only on the current state of the market and on external random elements.
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Simulace stochastických modelů hromadné obsluhy
Slámová, Kateřina ; Jablonský, Josef (advisor) ; Kuncová, Martina (referee)
Práce vystihuje teoretické poznatky z oblasti teorie hromadné obsluhy a simulace a následně jsou aplikovány poznatky do praxe. Pro případovou studii je využíván simulační software Simul8 a podpůrný program Crystal Ball, pomocí nichž je vytvořen model. Cílem je navrhnout nejlepší řešení daného problému a zhodnotit systém z hlediska struktury a funkčnosti. S modelem je provedeno několik experimentů a následně je posouzena vhodnost či nevhodnost použití jednotlivých variant.
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