This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times,in particular,forward and backward recurrence processes.We obtain the transient solution of the process in the fo...This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times,in particular,forward and backward recurrence processes.We obtain the transient solution of the process in the form of a generalized Markov renewal equation.A distinguishing feature is that Markov and semi-Markov processes result as special cases of the proposed model.To model the credit rating dynamics to demonstrate its applicability,we apply the proposed stochastic process to Standard and Poor’s rating agency’s data.Further,statistical tests confirm that the proposed model captures the rating dynamics better than the existing models,and the inclusion of recurrence times significantly impacts the transition probabilities.展开更多
This paper considers how to find some joint distributions and their marginal distributions of crossing time and renewal numbers related to two PH-renewal processes by constructing an absorbing Markov process.
A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc....A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.展开更多
The reliability of structural systems, lying in aggressive environments, changes over time. Proper maintenance is usually required to achieve a suitable performance level of life-cycle. The damage process affecting th...The reliability of structural systems, lying in aggressive environments, changes over time. Proper maintenance is usually required to achieve a suitable performance level of life-cycle. The damage process affecting the systems often suffers from uncertainty due to the randomness involved in each environmental attack. Therefore, basing on suitable damage modeling as well as on probabilistic analysis, the main features of time-variant deterioration process are modeled and then the life-cycle is assessed. On the basis of Markov renewal theory (MRT), this paper proposes a combined approach using an appropriate time dependent damage model and probabilistic analysis. Since repairing deteriorated structures requires the arrangement of maintenance strategies, possible selective maintenance scenarios have to be considered. Referring to the relationship between MRT and an appropriate condition index, some repair strategies have been proposed and compared with each other. Those strategies are applied just to seriously deteriorated members. Furthermore selective maintenance benefits are economically investigated.展开更多
Aspects of human behavior in cyber security allow more natural security to the user. This research focuses the appearance of anticipating cyber threats and their abstraction hierarchy levels on the mental picture leve...Aspects of human behavior in cyber security allow more natural security to the user. This research focuses the appearance of anticipating cyber threats and their abstraction hierarchy levels on the mental picture levels of human. The study concerns the modeling of the behaviors of mental states of an individual under cyber attacks. The mental state of agents being not observable, we propose a non-stationary hidden Markov chain approach to model the agent mental behaviors. A renewal process based on a nonparametric estimation is also considered to investigate the spending time in a given mental state. In these approaches, the effects of the complexity of the cyber attacks are taken into account in the models.展开更多
This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vect...This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.展开更多
文摘This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times,in particular,forward and backward recurrence processes.We obtain the transient solution of the process in the form of a generalized Markov renewal equation.A distinguishing feature is that Markov and semi-Markov processes result as special cases of the proposed model.To model the credit rating dynamics to demonstrate its applicability,we apply the proposed stochastic process to Standard and Poor’s rating agency’s data.Further,statistical tests confirm that the proposed model captures the rating dynamics better than the existing models,and the inclusion of recurrence times significantly impacts the transition probabilities.
文摘This paper considers how to find some joint distributions and their marginal distributions of crossing time and renewal numbers related to two PH-renewal processes by constructing an absorbing Markov process.
文摘A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.
文摘The reliability of structural systems, lying in aggressive environments, changes over time. Proper maintenance is usually required to achieve a suitable performance level of life-cycle. The damage process affecting the systems often suffers from uncertainty due to the randomness involved in each environmental attack. Therefore, basing on suitable damage modeling as well as on probabilistic analysis, the main features of time-variant deterioration process are modeled and then the life-cycle is assessed. On the basis of Markov renewal theory (MRT), this paper proposes a combined approach using an appropriate time dependent damage model and probabilistic analysis. Since repairing deteriorated structures requires the arrangement of maintenance strategies, possible selective maintenance scenarios have to be considered. Referring to the relationship between MRT and an appropriate condition index, some repair strategies have been proposed and compared with each other. Those strategies are applied just to seriously deteriorated members. Furthermore selective maintenance benefits are economically investigated.
文摘Aspects of human behavior in cyber security allow more natural security to the user. This research focuses the appearance of anticipating cyber threats and their abstraction hierarchy levels on the mental picture levels of human. The study concerns the modeling of the behaviors of mental states of an individual under cyber attacks. The mental state of agents being not observable, we propose a non-stationary hidden Markov chain approach to model the agent mental behaviors. A renewal process based on a nonparametric estimation is also considered to investigate the spending time in a given mental state. In these approaches, the effects of the complexity of the cyber attacks are taken into account in the models.
文摘This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.
