semi-Markov Approach Research Articles

Analytical model of a virtualized computing system using semi-markov approach

Analytical model of a virtualized computing system using semi-markov approach

A Semi-Markov Approach to Study a Group of Kinesin Motors.

We propose a general mathematical and computational approach to study cellular transport driven by a group of kinesin motors. It is a framework for multi-scale modeling that integrates kinetic models of single kinesin motors, including detachment and reattachment events, to study group behaviors of several motors. By formulating the problem as a semi-Markov process and applying a central limit theorem, asymptotic velocity and diffusivity can be readily calculated, which offers considerable computational advantage over Monte Carlo simulations in tasks such as parameter sensitivity analysis and model selection. We demonstrate the method with some examples. The importance of incorporating the intrinsic microscopic-level dynamics of individual motors is illustrated by showing how changes at the microscopic level propagate to the motor-cargo complex at a mesoscopic level. Particularly, we showcase an example in which changes in the second moment of single-motor characteristics gives rise to different first moment characteristics of the motor group.

Stochastic modeling and parameter estimation of turbogenerator unit of a thermal power plant under classical and Bayesian inferential framework.

The work reported in present study deals with the development of a novel stochastic model and estimation of parameters to assess reliability characteristics for a turbogenerator unit of thermal power plant under classical and Bayesian frameworks. Turbogenerator unit consists of five components namely turbine lubrication, turbine governing, generator oil system, generator gas system and generator excitation system. The concepts of cold standby redundancy and Weibull distributed random variables are used in development of stochastic model. The shape parameter for all the random variables is same while scale parameter is different. Regenerative point technique and semi-Markov approach are used for evaluation of reliability characteristics. Sufficient repair facility always remains available in plant as well as repair done by the repairman is considered perfect. As the life testing experiments are time consuming, so to highlight the importance of proposed model Monte Carlo simulation study is carried out. A comparative analysis is done between true, classical and Bayesian results of MTSF, availability and profit function.

Semi-Markov approach for reliability modelling of light utility vehicles

Vehicles are important elements of military transport systems. Semi-Markov processes, owing to the generic assumption form, are a useful tool for modelling the operation process of numerous technical objects and systems. The suggested approach is an extension of existing stochastic methods employed for a wide spectrum of technical objects; however, research on light utility vehicles complements the subject gap in the scientific literature. This research paper discusses a 3-state semi-Markov model implemented for the purposes of developing reliability analyses. Based on an empirical course of the operation process, model was validated in terms of determining the conditional probabilities of interstate transitions for an embedded Markov chain, as well as parameters of time distribution functions. The Laplace transform was used to determine the reliability function, failure probability density function, failure intensity, and expected time to failure. Readiness index values were calculated based on ergodic probabilities.

Modelling the Operation Process of Light Utility Vehicles in Transport Systems Using Monte Carlo Simulation and Semi-Markov Approach

This research paper presents studies on the operation process of the Honker 2000 light utility vehicles that are part of the Polish Armed Forces transport system. The phase space of the process was identified based on the assumption that at any given moment the vehicle remains in one of four states, namely, task execution, awaiting a transport task, periodic maintenance, or repair. Vehicle functional readiness and technical suitability indices were adopted as performance measures for the technical system. A simulation model based on Monte Carlo methods was developed to determine the changes in the operational states. The occurrence of the periodic maintenance state is strictly determined by a planned and preventive strategy of operation applied within the analysed system. Other states are implementations of stochastic processes. The original source code was developed in the MATLAB environment to implement the model. Based on estimated probabilistic characteristics, the authors validated 16 simulation models resulting from all possible cumulative distribution functions (CDFs) that satisfied the condition of a proper match to empirical data. Based on the simulated operation process for a sample of 19 vehicles over the assumed 20-year forecast horizon, it was possible to determine the functional readiness and technical suitability indices. The relative differences between the results of all simulation models and the results obtained through the semi-Markov model did not exceed 6%. The best-fit model was subjected to sensitivity analysis in terms of the dependence between functional readiness and technical suitability indices on vehicle operation intensity. As a result, the proposed simulation system based on Monte Carlo methods turned out to be a useful tool in analysing the current operation process of means of transport in terms of forecasts related to a current environment, as well as when attempting its extrapolation.

Cost Effectiveness of Durvalumab in Unresectable Stage III NSCLC: 4-Year Survival Update and Model Validation from a UK Healthcare Perspective.

BackgroundIn the phase III PACIFIC study, durvalumab improved survival versus placebo in patients with unresectable stage III non-small-cell lung cancer (NSCLC) whose disease had not progressed after platinum-based concurrent chemoradiotherapy. The appraisal by the UK’s National Institute for Health and Care Excellence (NICE) included a cost-effectiveness analysis based on an early data readout from PACIFIC [March 2018 data cut-off (DCO); median follow-up duration 25.2 months; range 0.2–43.1]. Uncertainties regarding long-term survival outcomes with durvalumab led to some challenges in estimating the cost effectiveness of this therapy.ObjectiveHere, we validate the survival extrapolations used in the original company base-case analysis by benchmarking them against updated survival data from the 4-year follow-up analysis of PACIFIC (i.e. approximately 4 years after the last patient was randomised; March 2020 DCO; median follow-up duration 34.2 months; range 0.2–64.9). Moreover, we update the original analysis with these more mature survival data to examine the consistency of key economic outputs with the original analysis.MethodsThe original analysis used a semi-Markov (state-transition) approach and was based on patients whose tumours expressed programmed cell death-ligand 1 on ≥ 1% of cells (to reflect the European licence for durvalumab). We benchmarked the survival extrapolations used in the original company base-case analysis against survival data from the 4-year follow-up of PACIFIC and updated the cost-effectiveness analysis with these more mature survival data. Early deaths avoided by the adoption of durvalumab into the UK Cancer Drugs Fund (CDF) in March 2019 were estimated using the 4-year follow-up survival data and an assumed uptake of 125 patients/year (lower estimate) and 367 patients/year (higher estimate).ResultsThe original company base-case analysis had a good visual fit with the observed overall survival (OS) distribution for the durvalumab arm and accurately predicted the 48-month OS rate (predicted 55%; observed 55%); by comparison, the fit was less precise for the placebo arm, for which the analysis underestimated the 48-month OS rate (predicted 32%; observed 38%). In the updated company base-case analysis, durvalumab yielded 2.51 incremental quality-adjusted life-years (QALYs) (− 0.43 vs. the original company base-case analysis), corresponding to an incremental cost-effectiveness ratio of £22,665/QALY (+£3298 vs. the original analysis), which falls within the upper bound of NICE’s willingness-to-pay threshold (£30,000/QALY gained). We estimate that between 31 and 91 early patient deaths may have been avoided by the adoption of durvalumab into the CDF.ConclusionsThese findings reinforce the patient benefit observed with durvalumab in unresectable stage III NSCLC, support the routine use and cost effectiveness of this therapy, and demonstrate how appropriate modelling can inform the early adoption of therapies by payers to achieve patient benefit.Supplementary InformationThe online version contains supplementary material available at 10.1007/s41669-021-00301-7.

Availability and reliability analysis of cloud computing under economic denial of sustainability (EDoS) attack: a semi-Markov approach

Economic denial of sustainability (EDoS) attack is a new type of distributed denial of service (DDoS) attack which targets the economic resources of cloud adopters by exploiting the auto-scaling features of the cloud. EDoS attack has become a significant threat to cloud adopters as it can lead to bankruptcy or withdrawal from cloud services and this in turn entails unavailability of the cloud services. In fact, availability has been one of the most significant issues of cloud computing securities. To address this issue caused by an EDoS attack, we develop a novel state-based availability model of the cloud under the EDoS attack with the help of a semi-Markov process. Based on the proposed model, we determine the steady state availability of the cloud under the EDoS attack. In addition, we derive the mean time to failure (or reliability) of the cloud in the presence of the EDoS attack to characterize the period of time for which the cloud adopter experiences the state of being bankrupt or service unsustainable situation. Moreover, we present a cost management strategy to prevent the cloud adopter from undergoing bankruptcy or experiencing unexpected exorbitant bill by incorporating the cloud shutdown feature into the proposed model. Numerical illustrations are presented which give insights into how availability and reliability of the cloud services are affected by the EDoS attack. The proposed model is also validated via simulation evidences.

Degrading systems availability analysis: analytical semi-Markov approach

This paper deals with modeling and analysis of complex mechanical systems that deteriorate with age. As systems age, the questions on their availability and reliability start to surface. The system is believed to suffer from internal stochastic degradation mechanism that is described as a gradual and continuous process of performance deterioration. Therefore, it becomes difficult for maintenance engineer to model such system. Semi-Markov approach is proposed to analyze the degradation of complex mechanical systems. It involves constructing states corresponding to the system functionality status and constructing kernel matrix between the states. The construction of the transition matrix takes the failure rate and repair rate into account. Once the steady-state probability of the embedded Markov chain is computed, one can compute the steady-state solution and finally, the system availability. System models based on perfect repair without opportunistic and with opportunistic maintenance have been developed and the benefits of opportunistic maintenance are quantified in terms of increased system availability. The proposed methodology is demonstrated for a two-stage reciprocating air compressor with intercooler in between, system in series configuration.

On the Integral of Diffusion Process on Interval with Unattainable Edges Boundaries: Semi-Markov Approach

A one-dimension semi-Markov process of diffusion type is considered. A range of values of this process is an open finite interval. It is supposed to have unattainable edges. The integral of this process as a function of time is studied. The invariance principle for this integral is proved.

Portfolio optimization of credit risky bonds: a semi-Markov process approach

This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds. The criteria to optimize the credit portfolio is based on l∞-norm risk measure and the proposed optimization model is formulated as a linear programming problem. The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process. Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models, i.e., it addresses the ageing effect present in the credit rating dynamics. The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds. The empirical performance of the proposed model is analyzed using the real data. Further, comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models.

Modeling the Heterogeneous Duration of User Interest in Time-Dependent Recommendation: A Hidden Semi-Markov Approach

Recommender systems are widely used for suggesting books, education materials, and products to users by exploring their behaviors. In reality, users’ preferences often change over time, leading to studies on time-dependent recommender systems. However, most existing approaches that deal with time information remain primitive. In this paper, we extend existing methods and propose a hidden semi-Markov model to track the change of users’ interests. Particularly, this model allows for capturing the different durations of user stays in a (latent) interest state, which can better model the heterogeneity of user interests and focuses. We derive an expectation maximization algorithm to estimate the parameters of the framework and predict users’ actions. Experiments on three real-world datasets show that our model significantly outperforms the state-of-the-art time-dependent and static benchmark methods. Further analyses of the experiment results indicate that the performance improvement is related to the heterogeneity of state durations and the drift of user interests in the dataset.

Downward migration credit risk problem: a non-homogeneous backward semi-Markov reliability approach

International organizations evaluate credit risk and rank firms according to risk by assigning them a ‘rating’. The time evolution of a rating can be studied by means of Markov models. Some papers have outlined the problem pertaining to the unsuitable fitting of Markov processes in a credit risk environment. This paper presents a model that overcomes the problems given by the Markov rating models. It includes non-homogeneity, the downward problem and the randomness of time in the transitions of states, thus making it possible to consider the duration inside a state in a complete way. In this paper, both, the transient and asymptotic analyses are presented. The asymptotic analysis is performed by using a mono-unireducible topological structure. Moreover, a real data application is conducted using the historical database of Standard & Poor’s as the source.

Semi-Markov Models for the Deterioration of Bridge Elements

AbstractMany bridge management systems (BMSs) use a Markov chain model to forecast the deterioration process. The Markov property may be considered to be restrictive when modeling the deterioration of transportation assets, primarily because of the memoryless property and assumption of exponential distribution for sojourn times in the condition states. This study addresses some of the limitations that arise from the use of purely Markov chain deterioration models for transportation infrastructure by introducing alternative approaches that are based on the semi-Markov process. Two semi-Markov approaches for modeling the deterioration of certain bridge elements are developed. These are compared against a previously developed semi-Markov approach, the traditional Markov chain deterioration approach, and the change in the average actual condition indices of bridge elements that deteriorated for 8 years after being constructed. The results obtained from this study indicated that semi-Markov models are feasible...

Tornadoes and related damage costs: statistical modelling with a semi-Markov approach

ABSTRACTWe propose a statistical approach to modelling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modelling the tornado intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornado intensity into six states, it is possible to model the tornado intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornado occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application, we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. The paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.

Semi-Markov Arnason–Schwarz Models

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis.

Semi-Markov Model of a Standby System with General Distribution of Arrival and Failure Times of Server

The aim of this paper is to develop a stochastic model of a cold standby system consisting of two identical units and a service facility, called server. This paper considers the failure of server during operation. The semi-Markov approach is explored to develop the probabilistic model and regenerative point technique is used to derive expressions for system’s performance measures such as mean time to system failure, availability, profit etc. In the model the server takes some time to arrive at the system. The server, while on job, may fail. Upon failure it goes for treatment and rejoins thereafter. Both the arrival and failure times follow general distribution with different probability distribution functions. The numerical illustration, for a particular case, points out that both the server arrival and failure times significantly affect the system performance.

Modeling and Performance Analysis of State Transitions for Energy-Efficient Femto Base Stations

Lowering the energy required by base stations (BSs) is one of the hot issues nowadays in order to achieve green cellular networks. The energy consumption of femto BSs can be reduced, by turning off the radio interface when there is no mobile station (MS) under the coverage area of the femto BSs or MSs served by the femto BSs do not transmit or receive data packets for a long time, especially late at night. In the energy-efficient femto BSs, if MSs have any data packet to transmit and the radio interface of femto BSs is in the off state, MSs wake up the radio interface of femto BSs by using an additional low-power radio interface. In this paper, active (data), idle, active (signaling), sleep entering, sleep and waking up states are defined for the state model for the energy-efficient femto BSs, and the state transitions are modeled analytically. The steady-state probability of each state is derived thoroughly using a semi-Markov approach. Then, the performance of the energy-efficient femto BSs is analyzed in detail, from the aspects of energy consumption, cumulative average delay, cost and low-power radio signaling load. From the results, the tradeoff relationship between energy consumption and cumulative average delay is analyzed in detail, and it was concluded that an appropriate inactivity timer value should be selected to balance the tradeoff.

Economic performance indicators of wind energy based on wind speed stochastic modeling

Abstract We propose the computation of different wind energy production indicators and financial profitability of potential wind power sites. The computation is performed by modeling the wind speed process as an indexed semi-Markov chain to predict and simulate the wind speed dynamics. We demonstrate that the indexed semi-Markov chain approach enables reproducing the indicators calculated on real data. Two different time horizons of 15 and 30 years are analyzed. In the first case we consider the government incentives on the energy price now present in Italy, while in the second case the incentives have not been taken into account.

Semi-Markov approach to the problem of delayed reflection of diffusion Markov processes

Semi-Markov approach to the problem of delayed reflection of diffusion Markov processes

Semi Markov Approach for Asymptotic Performance Analysis of a Standby System with Server Failure

this paper the asymptotic performance of a cold standby system with two identical units is analyzed. When a unit fails it is inspected by a server to check the feasibility of repair or replacement. If repair is not feasible, unit is replaced by new. The server is subjected to failure while performing its job. The system model is developed using semi-Markov approach of Markov processes. The regenerative point technique is used to derive expressions for various measures of system performance. The random variables associated with the system (failure time, inspection time, repair time, treatment time) are assumed to follow arbitrary distribution with different probability density functions. A numerical study is also presented to demonstrate the practical importance of the research.