semi-Markov System Research Articles

Asymptotic Behavior of First Passage Probabilities in the Perturbed Non-homogeneous Semi-Markov Systems

In the present we study the asymptotic behavior of the sequence of the first passage probability matrices in a Perturbed Non-Homogeneous Semi-Markov System (P-NHSMS). We study initially triple sequences of matrices and we establish a basic result which provides the conditions under which the triple limit of a sequence coinsides. Then we provide some theorems which establish the asymptotic behavior of the sequence of matrices of the expected probabilities of first visit in a state in a given interval with a specified number of transitions.

Stationary availability of a semi-Markov system with random maintenance

We consider a reparable system with a finite state space, evolving in time according to a semi-Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi-regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.

The closed continuous-time homogeneous semi-Markov system as a non-Newtonian fluid

The closed continuous-time homogeneous semi-Markov system as a non-Newtonian fluid

The closed continuous‐time homogeneous semi‐Markov system as a non‐Newtonian fluid

The set of the attainable structures of a closed continuous-time homogeneous semi-markov system (HSMS) with n states, is considered as a continuum and the evolution of the HSMS in the Euclidean space En corresponds to its motion. In accordance with the velocity field of the HSMS, a suitable model of a continuum—defined by an acceleration-dependent stress tensor of the form T = −pI + 2μM and satisfying the Cauchy's equation of motion—is proposed in order to explain the motion of the HSMS. Then, the variation of the internal, kinetic and total energy of the model is examined. Copyright © 2000 John Wiley & Sons Ltd.

On semi-markov compartmental models with branching particles under the influence of disasters

A semi-Markov multi-compart mental system in which particles reproduce similar particles as a Markov branching process and being subjected to disasters is studied. Expressions for the mean number of particles alive at time t in each compartment are obtained. The results concerning irreversible, mammillarian and catenary compartmental systems have been discussed.

Counting transitions—entrance probabilities in non-homogeneous semi-Markov systems

In the present paper, the concept of the number of transitions in a non-homogeneous semi-Markov system is introduced. Then the problem of finding the equations that describe the expected population structure, in relation with the number of transitions, is studied. Also, the entrance probabilities of the system are defined and their limit is provided, under certain conditions. © 1998 John Wiley & sons, Ltd.

Non-parametric estimation for semi-Markov kernels with application to reliability analysis

The authors consider an irreducible Markov renewal process (MRP) with a finite number of states. Their aim is to derive estimators of a censored MRP with a finite number of states either in a fixed time T or in the Nth jump. The estimators given here are seen to be of the Kaplan-Meier type. The asymptotic properties these estimators are given. The reliability of a semi-Markov system model is examined numerically by the estimators, and a comparison is made with estimators obtained by Lagakos et al. © 1996 John Wiley & Sons, Ltd.

Asymptotic behavior of nonhomogeneous semi-Markov systems

We study the asymptotic behavior of a nonhomogeneous semi-Markov system (population) in discrete time. After a series of definitions, lemmas, and theorems, we firstly establish the conditions under which the ergodic behavior of a nonhomogeneous semi-Markov chain exists and then find the limit of the basic matrix of the chain Q( n, s) in closed form. Finally, the existence of the asymptotic population structure of the nonhomogeneous semi-Markov system is studied, and the limit is provided in closed analytic form.

On the total sojourn time of particles in semi-markov compartmental system with branching particles

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.

Non-homogeneous semi-Markov systems and maintainability of the state sizes

In this paper we introduce and define for the first time the concept of a non-homogeneous semi-Markov system (NHSMS). The problem of finding the expected population stucture is studied and a method is provided in order to find it in closed analytic form with the basic parameters of the system. Moreover, the problem of the expected duration structure in the state is studied. It is also proved that all maintainable expected duration structures by recruitment control belong to a convex set the vertices of which are specified. Finally an illustration is provided of the present results in a manpower system.

Non-homogeneous semi-Markov systems and maintainability of the state sizes

In this paper we introduce and define for the first time the concept of a non-homogeneous semi-Markov system (NHSMS). The problem of finding the expected population stucture is studied and a method is provided in order to find it in closed analytic form with the basic parameters of the system. Moreover, the problem of the expected duration structure in the state is studied. It is also proved that all maintainable expected duration structures by recruitment control belong to a convex set the vertices of which are specified. Finally an illustration is provided of the present results in a manpower system.

Filtering of a semi-Markov queueing system with retrials

A recursive differential equation for the conditional probability of the number of waiting customers is derived for the MwrM|G|1 queue with continuous monitoring of the server state.

The total sojourn time distribution in a stochastic compartmental model

The total time spent by both a single particle and by all the particles up to an instant t in a particular compartment in a semi-Markov compartmental system is discussed. Special cases are also considered.