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Maintaining a reliable water treatment plant is paramount for a consistent and dependable supply of safe drinking water to communities. This study employs an integrated approach, leveraging advanced methodologies including Markov processes, supplementary variable technique, and Laplace transformation. The research seeks to comprehensively model the plant’s dynamic behavior, transitions between operational states, and the influence of maintenance practices. By employing these methodologies, the research aims to enhance the precision of critical reliability metrics such as reliability and availability. The study further incorporates thorough cost analysis, shedding light on the economic implications of reliability-enhancing measures. Additionally, sensitivity analysis is employed to identify critical variables influencing plant performance and economic efficiency. The insights garnered from this study are expected to provide a sophisticated understanding of the water treatment plant’s performance, fostering effective decision-making strategies to optimize maintenance protocols and ensure the uninterrupted delivery of clean and secure water to communities.

Due to the improvement of seismic design standards, viscoelastic dampers have been rapidly developed and widely applied in bridge structures. Currently, there is limited research on dynamic reliability analysis of large bridge structures equipped with fractional-order dampers. In this paper, a hybrid method combining the time-domain explicit method and Markov process is proposed for the dynamic reliability analysis of multi-span continuous girder bridges with fractional-order dampers under non-stationary random excitation. This method introduces a fractional damping system and non-stationary random excitation to simulate both the bridge structure and external forces. The response coefficient matrix of the fractional damping structure is solved using the time-domain explicit method, and the response variance is directly calculated using the moment algorithm. The dynamic reliability analysis is then performed by applying the Markov process based on the structural response variance. Compared to traditional methods for structural dynamic reliability analysis, this approach offers higher computational efficiency and greater accuracy. By analyzing the response variance and dynamic reliability of a four-span continuous girder bridge equipped with viscoelastic dampers, the proposed method is validated using the Monte Carlo method.

In financial network models, to assess systemic risk, a general understanding and prediction of precisely how a single financial institution is associated with systemic risk from the network perspective remains lacking. This paper proposes a framework for predicting and assessing system crises through inferring the cause–effect relationships between financial institutions and system state, which is structured in three steps: the assessment stage for system state based on the mean-variance framework, the prediction stage based on a Bayesian network and the reliability stage based on the Markov process. By applying them to monthly returns of financial institutions, it implies the need to pay attention to insurance and Broker sectors while regulating the banking system on the Bayesian network theory. Moreover, we find that the measure contains predictive power both during tranquil periods and during financial crisis periods. The results can be applied to derive interventions in financial crisis management with regard to systemic risk prediction and system state reliability.

In this paper, a stochastic SEIR epidemic model on heterogeneous networks is established, and the law of large numbers and the central limit theorem of the epidemic process are obtained. By using the random time transformation, the mean behavior of the epidemic process is analyzed, that is, the solution of the deterministic model is given. Further, the asymptotic distribution of the final size is provided. Then, the network-based stochastic epidemic model is applied to a COVID-19 infection at a construction site in Qingpu District of Shanghai, and the parameters of the model are estimated by fitting the data of confirmed cases. Based on the estimated parameter values, the intervention measure implemented at the site is assessed by numerical simulations, and we find that the intervention does not effectively curb the development of the disease. In addition, simulation results show that the asymptotic approximation for the final size is good. The impact of the detecting or symptomatic rate on the final size is also analyzed by numerical studies. The results indicate that as the rate increases, the mean of the final size decreases and the variance increases, which is more conducive to controlling the spread of the disease.

We extend the Sznajd Model for opinion formation by introducing persuasion probabilities for opinions. Moreover, we couple the system to an environment which mimics the application of the opinion. This results in a feedback, representing single-state opinion transitions in opposite to the two-state opinion transitions for persuading other people. We call this model opinion formation in an open community (OFOC). It can be seen as a stochastic extension of the Sznajd model for an open community, because it allows for a special choice of parameters to recover the original Sznajd model. We demonstrate the effect of feedback in the OFOC model by applying it to a scenario in which, e.g., opinion B is worse then opinion A but easier explained to other people. Casually formulated we analyzed the question, how much better one has to be, in order to persuade other people, provided the opinion is worse. Our results reveal a linear relation between the transition probability for opinion B and the influence of the environment on B.

The AutoRegressive Conditional Heteroskedasticity (ARCH) and its generalized version (GARCH) family of models have grown to encompass a wide range of specifications, each of them is designed to enhance the ability of the model to capture the characteristics of stochastic data, such as financial time series. The existing literature provides little guidance on how to select optimal parameters, which are critical in efficiency of the model, among the infinite range of available parameters. We introduce a new criterion to find suitable parameters in GARCH models by using Markov length, which is the minimum time interval over which the data can be considered as constituting a Markov process. This criterion is applied to various time series and its results support the known idea that GARCH(1, 1) model works well.

We study the train aggregation behavior in a railway subsystem using the Markov approach. This approach is different from the queue theory, which is a main method to design some railway subsystems in the literature. With some simple assumptions, we solve the corresponding master equation describing the train aggregation behavior. Using the least square trigonometric approximation, we construct a continuous rate function for a real example, and show the evolution of the size of train cluster with time. Also the variance and relative error of the train aggregation are calculated.

We have used standard fractal analysis and Markov approach to obtain further insights on roughness and multifractality of different surfaces. The effect of coating rates on generating topographic rough surfaces in copper thin films with same thickness has been studied using atomic force microscopy technique (AFM). Our results show that by increasing the coating rates, correlation length (grain sizes) and Markov length are decreased and roughness exponent is decreased and our surfaces become more multifractal. Indeed, by decreasing the coating rate, the relaxation time of embedding the particles is increased.

We analyzed to identify the determinants affecting the presale rate in the housing projects and verified whether there are differences in the determinants of that by regimes. We found that the effects of determinants, such as the ratio of the new apartments’ sales price to existing apartments’ prices, educational environment, the number of unsold houses, and the interest rate of a mortgage on the initial presale rate, could have been different depending on which regime the housing market belongs to. This suggests that the government in Korea and Asian countries should consider the differentiation in effects of the determinants depending on the regime when the government tries to make housing policies.

We present two models for studying a system maintained by means of imperfect repairs before a replacement or a perfect repair is allowed. The operational and repair times follow phase-type distributions. Imperfect repair means that successive operational times decrease and successive repair times increase. Under these assumptions, models that govern the systems are Markov processes, whose structures are determined, and several performance measures are calculated in transient and stationary regime. These models extend other previously studied in the literature. The incorporation of phase-type distributions allows to apply the model to many other distributions. A numerical example illustrates the calculations and allows a comparison of the results.

We propose the performance evaluation method for the multi-task system with software reliability growth process. The software fault-detection phenomenon in the dynamic environment is described by the Markovian software reliability model with imperfect debugging. We assume that the cumulative number of tasks arriving at the system follows the homogeneous Poisson process. Then we can formulate the distribution of the number of tasks whose processes can be complete within a prespecified processing time limit with the infinite-server queueing model. From the model, several quantities for software performance measurement considering the real-time property can be derived and given as the functions of time and the number of debuggings. Finally, we present several numerical examples of the quantities to analyze the relationship between the software reliability characteristics and the system performance measurement.

Service availability is one of the customer-oriented attribute and defined as the attribute that the system can successfully satisfy the customers' requests. This paper discusses the stochastic service availability measurement for the computer-based system incorporating the concept of hardware/software codesign. We assume that the computer-based system consists of one hardware subsystem and one software subsystem and consider the situation where one customer intermittently uses the system which is operating and available anytime. From the viewpoint of a customer, occurrence of a system failure is recognized when either one of the following two events arises: A system failure occurs when the customer is using the system, or a usage request occurs when the system is down. We propose and derive three kinds of novel service-oriented system availability assessment measure. These are given as the functions of time and the number of software debuggings. The time-dependent behaviors of the system alternating between up and down states and the customer's request are described by a Markov process. Especially for the software subsystem, we incorporate the dynamic software reliability growth process, the upward tendency of difficulty in debugging, and the imperfect debugging environment into the model. Finally, we present several numerical examples of these measures for system service availability analysis.

In this paper, we study a passenger–taxi matching queue system. The system is modeled as a birth-and-death process. Since the system is so complex, we mainly focus on numerical analysis. A centralized system and a decentralized one are considered. In the centralized system, the government sets thresholds for both passengers and taxis to maximize the social welfare. We analyze the performance measures of this model, discuss the range of two thresholds that ensures positive social welfare, and numerically give the upper bound of threshold. In the decentralized system, passengers and taxis determine whether to join the system or balk based on their individual utility functions. Further, we consider the government’s tax and subsidy to the taxi drivers. Numerical results show that the social welfare function in the centralized system is concave with respect to the thresholds and the government central planning benefits the society. In the decentralized system, no matter what the passenger and taxi arrival rates are, the social welfare is concave with respect to the taxi fare. Moreover, we analyze the effect of the arrival rates and the benefits of the tax and subsidy.

In recent years, the structure of multi-phase buck converter also called Interleaved Buck Converter (IBC) has gained considerable attention. The advantages of the IBC in comparison to the conventional Buck converter (CBC) are the lower output current ripple, higher efficiency, fast transient response, lower electromagnetic interference and higher reliability. Since more than one stage is employed in the IBC, this converter is highly reliable. In this paper, the reliability and mean time to failure (MTTF) of the CBC, and two- and three-stage IBCs are figured out. Using the obtained results and considering various scenarios, a comprehensive comparison is provided. In addition, the operation of the converter in case of fault occurrence for high and low capacities is analyzed and reliability is evaluated in each state. The relation between the reliability and temperature of semiconductor elements is discussed. Furthermore, a laboratory-scaled prototype is used to extract the experimental results of the temperature variation of the elements during a fault. Markov model is used to evaluate the analyzed reliability.

The paper proposes a systematic solution to the problem of mixing different stochastic processes, each implied by a certain mode of operation of the system at hand and with a random duration whose distribution depends on the previous and present modes. We do so by widening the scope of an existing framework for the statistical characterization of finite valued processes with memory-one properties. The point of view is that of stochastic dynamics and the state space of the process is partitioned into regions (that we identify with modes) such that, if sojourn in a mode can be assumed, the statistical characterization is fully understood. The process is also allowed to stochastically move from one mode to another and the number of time steps for which it remains in each mode is a random variable whose distribution is a function only of the mode visited before. A general theoretical framework is developed here for the computation of any-order joint probabilities. The framework is then exemplified for the case of locally looping systems that are random sequences of modes comprising the cyclical execution of given atomic actions. They are the model of choice for complex appliances that operate following the steps of a communication protocol, and/or the various phases of a bus cycle, and/or the load-compute-store mechanism of a microprocessor, etc. Exploiting the theory put forward by the paper, we highlight how these processes could be generated by suitably designed 2-d chaotic maps and how their second- and third-order spectra may be obtained and interpreted when exponentially or polynomially decaying distributions are assumed for mode sojourn times.

A Markov chain model is constructed to simulate pattern formation arising from an evolutionary population of interactive homogeneous agents. In the structure of optimal evolution and stochastic properties, the model exhibits emergent properties with rich dynamical diagrams. We study the cluster splitting transition with the coarsening period-adding phenomena shown by the model, which gives an example of pattern formation in the evolution of complex system and reveals dynamical behavior of the Markov chain process.

In this paper, we study random dynamical systems generated by two Allee maps. Two models are considered — with and without small random perturbations. It is shown that the behavior of the systems is very similar to the behavior of the deterministic system if we use strictly increasing Allee maps. However, in the case of unimodal Allee maps, the behavior can dramatically change irrespective of the initial conditions.

Selecting an appropriate mathematical model to describe the dynamical behavior of a genetic regulatory network plays an important part in discovering gene regulatory mechanisms. Whereas fine-scale models can in principle provide a very accurate description of the real genetic regulatory system, one must be aware of the availability and quality of the data used to infer such models. Consequently, pragmatic considerations motivate the selection of a model possessing minimal complexity among those capable of capturing the level of real gene regulation being studied, particularly in relation to the prediction capability of the model. This paper compares fine-scale stochastic-differential-equation models with coarse-scale discrete models in the context of currently available data and with respect to their description of switch-like behavior among specific groups of genes.

We discuss the software availability modeling when the system is used intermittently. From the viewpoint of users, occurrence of a system failure is recognized when the event that either a software failure occurs when the system is in use or a usage demand occurs when the system is under restoration arises. In this pape, a couple of new measures for software availability assessment are derived; these are called the disappointment probabilities in use and under restoration, respectively. It is supposed that the usage demand of the system occurs randomly and that the user's demand duration is also random. The time-dependent behavior of the system alternating between up and down states is described by a Markov process. Then the software reliability growth process, the upward tendency in difficulty of debugging, and the imperfect debugging environment are also considered.

Electricité de France produces about 75% of its electricity with nuclear power plants. Some hydraulic plants and most fossil fuel power plants are used to pass electricity consumption peaks. Therefore these facilities are required only intermittently. For such systems, a breakdown does not result in a production loss during a standby period. This particular feature is not taken into account by conventional availability evaluation methods. The objective of this paper is to introduce a definition of availability which holds in such a context, and to describe a mathematical method suited to the calculation of this new definition of availability.