Probabilistic Analysis of Long-Term Climate Drought Using Steady-State Markov Chain Approach

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. The authors assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.

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Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks

Comparative and Functional Genomics ◽

10.1002/cfg.342 ◽

2003 ◽

Vol 4 (6) ◽

pp. 601-608 ◽

Cited By ~ 87

Author(s):

Ilya Shmulevich ◽

Ilya Gluhovsky ◽

Ronaldo F. Hashimoto ◽

Edward R. Dougherty ◽

Wei Zhang

Keyword(s):

Markov Chain ◽

Steady State ◽

Markov Chains ◽

Regulatory Networks ◽

Boolean Networks ◽

Genetic Regulatory Networks ◽

Long Run ◽

Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.

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DEVELOPING AND CALIBRATING A STOCHASTIC RAINFALL GENERATOR MODEL FOR SIMULATING DAILY RAINFALL BY MARKOV CHAIN APPROACH

Jurnal Teknologi ◽

10.11113/jt.v76.5946 ◽

2015 ◽

Vol 76 (15) ◽

Cited By ~ 1

Author(s):

N. S. Dlamini ◽

M. K. Rowshon ◽

Ujjwal Sahab ◽

A. Fikri ◽

S. H. Lai ◽

...

Keyword(s):

Markov Chain ◽

Production Systems ◽

Transition Probabilities ◽

Daily Rainfall ◽

Rainfall Series ◽

Climate Data ◽

Management Tools ◽

Stochastic Weather Generator ◽

Markov Chain Approach

Rainfall is an important parameter in tropical humid regions for which paddy production systems depend. A significant portion of paddy water requirements is supplied by natural rainfall. Several studies have predicted changes in rainfall patterns and in the amount of rain that may be obtainable in future owing to climate change. There is increased concern about future water availability for an important crop such as rice. Need to develop new water management tools for sustainable production is inevitable, but such tools require long-term climate data that is credible and consistent with the time. This study concerns itself with evaluating a stochastic weather generator (WGEN) model for simulating daily rainfall series. The model is assessed using long-term historical rainfall data obtained from a rice growing irrigation schemes in Malaysia. The model is based on a first-order two-state Markov chain approach which uses two transition probabilities and random number to generate rainfall series. Selected statistical properties were computed for each station and compared against those retrieved from the model after model training and testing. The results obtained from these comparisons are quite satisfactory giving confidence about the performance and future outputs from the model. The model has shown good skill in describing the rainfall occurrence process and rainfall amounts for the area. The model will be adapted in a subsequent study for downscaling and simulating effective daily rainfall series corresponding to future climate scenarios.

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Using the Markov Chain to Analyze Precipitation and Groundwater Drought Characteristics and Linkage with Atmospheric Circulation

Sustainability ◽

10.3390/su11061817 ◽

2019 ◽

Vol 11 (6) ◽

pp. 1817 ◽

Cited By ~ 5

Author(s):

Hsin-Fu Yeh ◽

Hsin-Li Hsu

Keyword(s):

Markov Chain ◽

Steady State ◽

Atmospheric Circulation ◽

River Basin ◽

Drought Characteristics ◽

Groundwater Drought ◽

The Future ◽

Southern Taiwan ◽

The Mean

In recent years, Taiwan has been facing water shortages due to the impact of climate change, which has resulted in many serious drought events, especially in southern Taiwan. Long-term records from 25 rainfall stations and 17 groundwater stations in the southern Taiwan basin were used in this study. We used the Standardized Precipitation Index (SPI) and the Standardized Groundwater Level Index (SGI) and employed the first-order Markov chain model and wavelet transform to determine the drought characteristics and propagation, including the steady-state probabilities of drought events and the mean duration for each station. The Drought Index (DI) was also used to investigate the effects of rainfall on groundwater drought. The results show that the steady-state probability of the meteorological drought in the Yanshui River basin in southern Taiwan is higher than that in other basins. The area with the longer mean duration is located in the Yanshui River basin and the Erren River basin, and overall, the mean duration ranges from 3 to 7 months. In addition, the results from the drought proneness analysis indicated that when rainfall causes a longer drought duration, there will be a higher degree of proneness to groundwater drought in the future. Finally, the results show that the mean duration of groundwater droughts are longer than those of meteorological droughts. The results of the wavelet analysis revealed a positive correlation at long-term scales, which may be related to large-scale atmospheric circulation. The information from this research could be used as a reference for water resource management in the future.

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Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

Encyclopedia of Information Science and Technology, Fourth Edition ◽

10.4018/978-1-5225-2255-3.ch136 ◽

2018 ◽

pp. 1570-1583

Author(s):

Khalid Alnowibet ◽

Lotfi Tadj

Keyword(s):

Markov Chain ◽

Steady State ◽

Performance Measures ◽

Threshold Level ◽

System Size ◽

State System ◽

Markov Chain Approach ◽

Optimal Value ◽

Two Phases ◽

Random Breakdowns

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. We assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.

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MULTI-STATE START-UP DEMONSTRATION TESTS

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539311004020 ◽

2011 ◽

Vol 18 (02) ◽

pp. 99-117 ◽

Cited By ~ 12

Author(s):

MICHELLE L. DEPOY SMITH ◽

WILLIAM S. GRIFFITH

Keyword(s):

Markov Chain ◽

Probabilistic Analysis ◽

Early Termination ◽

Test Results ◽

Practical Advantage ◽

Markov Chain Approach ◽

Start Up ◽

Practical Guidance ◽

Start Ups

Multistate start-up demonstration tests are proposed and analyzed using a Markov Chain approach. The new demonstration tests are generalizations of the CSTF, TSTF, and CSCF start-up demonstration tests discussed in the literature that have the important practical advantage of allowing for early termination when the quality of successful start-ups is exceptional. When the termination results in acceptance of the equipment, the use of a multi-state startup demonstration test results in an increase in the probability of an early termination of as much as. 35 over the optimal binary start-up test in cases studied. The Markov Chains methodology is used in the probabilistic analysis. Practical guidance on choosing tests, estimation, and comparisons of the various criteria are studied. The Markov Chain approach is then extended to study the non-i.i.d. case.

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Comparison of dynamic programming policies for long-term hydrothermal scheduling of single-reservoir systems in steady-state regime

Electric Power Systems Research ◽

10.1016/j.epsr.2021.107275 ◽

2021 ◽

Vol 196 ◽

pp. 107275

Author(s):

Thayze D’Martin Costa ◽

Secundino Soares

Keyword(s):

Dynamic Programming ◽

Steady State ◽

Steady State Regime ◽

Hydrothermal Scheduling ◽

Reservoir Systems ◽

State Regime

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Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care

Risks ◽

10.3390/risks9020037 ◽

2021 ◽

Vol 9 (2) ◽

pp. 37

Author(s):

Manuel L. Esquível ◽

Gracinda R. Guerreiro ◽

Matilde C. Oliveira ◽

Pedro Corte Real

Keyword(s):

Markov Chain ◽

Continuous Time ◽

Long Term Care ◽

Transition Probabilities ◽

Markov Chain Model ◽

Chain Model ◽

Chain Process ◽

Term Care ◽

National Network

We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.

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Approximating the stationary distribution of an infinite stochastic matrix

Journal of Applied Probability ◽

10.2307/3214743 ◽

1991 ◽

Vol 28 (1) ◽

pp. 96-103 ◽

Cited By ~ 25

Author(s):

Daniel P. Heyman

Keyword(s):

Markov Chain ◽

Steady State ◽

Stationary Distribution ◽

Numerical Approximation ◽

Stochastic Matrix ◽

Sufficient Conditions ◽

Finite System ◽

Balance Equations ◽

The Given ◽

Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

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