Applications on branching processes
Branching processes are stochastic processes with main difference among other stochastic processes that the systems that they can model have a special construction: a single individual lives for a unit of time and by its death produces 𝑛������ identical copies of itself. According to that principle...
Αποθηκεύτηκε σε:
| Κύριος συγγραφέας: | |
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| Άλλοι συγγραφείς: | |
| Γλώσσα: | English |
| Δημοσίευση: |
2022
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| Θέματα: | |
| Διαθέσιμο Online: | http://hdl.handle.net/11610/22796 |
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| Περίληψη: | Branching processes are stochastic processes with main difference among other stochastic processes that the systems that they can model have a special construction: a single individual lives for a unit of time and by its death produces 𝑛������ identical copies of itself. According to that principle and based on the relevant branching literature, branching processes are considered as a classical approximation for epidemics, biology, physics etc. The aim of this master thesis is to study in depth a type of stochastic processes, the branching processes, and focus on the existing applications, which would allow us to examine how these processes specifically are implemented and detect the strengths of branching processes comparing to other stochastic models. Additionally, primary scope constitutes the implementation of those processes in two different application areas.
After an extensive search of the relevant branching processes’ literature, we obtained that modeling and evaluating system reliability by using these processes seems to be poorly documented. This is the reason why the first part of this research focuses on the application of branching process on system reliability. In particular, we examine a refinery pump system reliability through branching processes. A Markov model is used to formulate real data from a petrochemical industry and be able to use them as inputs to the branching model. Through this application, a refinery pump system availability is discussed in an alternative perspective than in typical reliability theory. The probability of ultimate extinction of that peculiar population consisting of pumps as well as the failure probability of the system during a year are estimated as typical properties of branching processes. Among other findings, that are concentrated to system availability, is that comparing to other stochastic models, a branching process approximation of the system reliability could be profitable for the maintenance departments, as an alternative perspective, because through the expected number of working components and the probability of extinction, the reliability of an entire industry unit is discussed.
Moreover, motivated by the sudden outbreak of the Covid-19 pandemic incidence and based on the fact that branches processes are extensively used to model dynamics of epidemics, another application these processes, refering to a typical branching approximation of the coronavirus (covid-19) spread in Greece is also presented. For this epidemiology model application, by using branching processes and their main properties, important factors are estimated for the virus transmission in Greece, such as the basic and effective reproduction numbers along with the probabilities of the extinction and an outbreak. Based on these factors and on an additional non-mitigation scenario, the effectiveness of control measures is discussed. Overviewing the results revealed that the virus transmission was aggressive, however the control measures were effective. This statement is supported by the values of the aforementioned indicators.
In general, the contribution of this research is based οn three pillars. First of all, an analytical theoretical framework of branching processes is presented. Secondly, it provides knowledge about how to formulate and provide reliable results of a real problem in an alternative area of application for these processes, such as the mechanical system reliability. Finally, based on the fact that the presented branching models are consisting of different populations and thus the notion of parameters such as the expected number of population and the probability of extinction differ, we can assume that this research gives a comprehensive view of branching processes dynamics compared to other stochastic processes. Finally, according to the findings of those implementations, ideas for future work are extensively presented. |
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