scholarly journals The Mercury Environment: A Modeling Tool for Performance and Dependability Evaluation

2021 ◽  
Author(s):  
Thiago Pinheiro ◽  
Danilo Oliveira ◽  
Rubens Matos ◽  
Bruno Silva ◽  
Paulo Pereira ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Markov Chains ◽  
Mathematical Models ◽  
Discrete Time ◽  
Stochastic Petri Nets ◽  
System Behavior ◽  
Fault Trees ◽  
Flow Models ◽  
Dependability Evaluation ◽  
Reliability Block Diagrams

It is important to be able to judge the performance or dependability metrics of a system and often we do so by using abstract models even when the system is in the conceptual phase. Evaluating a system by performing measurements can have a high temporal and/or financial cost, which may not be feasible. Mathematical models can provide estimates about system behavior and we need tools supporting different types of formalisms in order to compute desired metrics. The Mercury tool enables a range of models to be created and evaluated for supporting performance and dependability evaluations, such as reliability block diagrams (RBDs), dynamic RBDs (DRBDs), fault trees (FTs), stochastic Petri nets (SPNs), continuous and discrete-time Markov chains (CTMCs and DTMCs), as well as energy flow models (EFMs). In this paper, we introduce recent enhancements to Mercury, namely new SPN simulators, support to prioritized timed transitions, sensitivity analysis evaluation, several improvements to the usability of the tool, and support to DTMC and FT formalisms.

Information System Availability

2017 ◽  
pp. 1-33
Keyword(s):  
Information System ◽  
Information Systems ◽  
Markov Chains ◽  
Short Introduction ◽  
System Availability ◽  
Fault Trees ◽  
Reliability Block Diagrams ◽  
Availability Modeling

In order to provide better understanding of the availability concept, it is necessary to define and review the terms that shape a framework for information systems availability. This section introduces the concept of availability and the three terms that are most associated with the concept of availability, namely: dependability, reliability and maintainability. A short introduction to availability modeling is also presented in this section by explaining three most widely used methods: Reliability Block Diagrams, Fault Trees Diagrams, and Markov Chains.

Discrete-time Markov chains

2011 ◽  
pp. 1-184
Author(s):  
Yuri Suhov ◽  
Mark Kelbert
Keyword(s):  
Markov Chains ◽  
Discrete Time

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

scholarly journals The effects of flooding and weather conditions on leptospirosis transmission in Thailand

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sudarat Chadsuthi ◽  
Karine Chalvet-Monfray ◽  
Anuwat Wiratsudakul ◽  
Charin Modchang
Keyword(s):  
Sensitivity Analysis ◽  
Public Education ◽  
Mathematical Models ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Weather Conditions ◽  
Transmission Dynamics ◽  
Multiplication Rate ◽  
High Degree ◽  
Transmission Models

AbstractThe epidemic of leptospirosis in humans occurs annually in Thailand. In this study, we have developed mathematical models to investigate transmission dynamics between humans, animals, and a contaminated environment. We compared different leptospire transmission models involving flooding and weather conditions, shedding and multiplication rate in a contaminated environment. We found that the model in which the transmission rate depends on both flooding and temperature, best-fits the reported human data on leptospirosis in Thailand. Our results indicate that flooding strongly contributes to disease transmission, where a high degree of flooding leads to a higher number of infected individuals. Sensitivity analysis showed that the transmission rate of leptospires from a contaminated environment was the most important parameter for the total number of human cases. Our results suggest that public education should target people who work in contaminated environments to prevent Leptospira infections.

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