Non-homogeneous semi-Markov System Research Articles

The augmented semi-Markov system and its asymptotic behaviour

This paper suggests a generalized semi-Markov model for manpower planning, which could be adopted in cases of unavailability of candidates with the desired qualifications/experience, as well as in cases where an organization provides training opportunities to its personnel. In this context, we incorporate training classes into the framework of a non-homogeneous semi-Markov system and we introduce an additional, external semi-Markov system providing the former with potential recruits. For the model above, referred to as the Augmented Semi-Markov System, we derive the equations that reflect the expected number of persons in each grade and we also investigate its limiting population structure. An illustrative example is provided. Copyright © 2010 John Wiley & Sons, Ltd.

Economic Rewards in Non-homogeneous Semi-Markov Systems

In this paper, a general reward model for a non homogeneous semi-Markov system will be provided. Both discrete and continuous time models will be studied considering reward to be a random variable of the economic type associated with the state occupancies and transitions. Basic equations will be exhibited and the main formulas for the expected reward that the system will generate in some interval of time (with and without discounting) will be determined for the discrete and continuous cases and a method is provided in order to find it in closed analytic form in relation with the basic parameters of the system. Also, results will be obtained for the expected reward per time period for the steady state.

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.

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.

The evolution of the theory of non‐homogeneous Markov systems

A review of the evolution of the theory of non-homogeneous Markov systems (NHMSs) is given. It starts with the definition of the stochastic process NHMS, discusses the variability of the process and provides as examples some real applications of the theory. Then, important novel ideas and basic theorems are presented on: (i) the asymptotic behaviour of NHMSs; (ii) control theory; (iii) cyclic behaviour; (iv) physics of populations: stability, entropy, energy; (v) non-homogeneous semi-Markov systems; (vi) the NHMS in a stochastic environment. © 1998 John Wiley & Sons, Ltd.

The evolution of the theory of non-homogeneous Markov systems

A review of the evolution of the theory of non-homogeneous Markov systems (NHMSs) is given. It starts with the definition of the stochastic process NHMS, discusses the variability of the process and provides as examples some real applications of the theory. Then, important novel ideas and basic theorems are presented on: (i) the asymptotic behaviour of NHMSs; (ii) control theory; (iii) cyclic behaviour; (iv) physics of populations: stability, entropy, energy; (v) non-homogeneous semi-Markov systems; (vi) the NHMS in a stochastic environment. © 1998 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.

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.

Rapprochement of consolidated stochastic systems and nonhomogeneous semi-Markov systems

The problem of asymptotic consolidation has been considered in a large number of investigations; they can be divided into three directions. In [I-3] one develops an analytic approach, connected with the investigation of the behavior of the solutions of the Markov renewal equations, which operates effectively at the analysis of homogeneous Markov processes (MP) and semi-Markov processes (SMP). In [4, 5], by direct probabilistic methods one has obtained a rapproachement of the characteristics of a consoliated process and of a process of the SMP type for processes with a discrete set of states. In [6-9] one has developed a new approach to the problems of asymptotic consolidation, making use of a special class of processes, viz., switching processes, which is effectively applied in [~0-12] to the analysis of both homogeneous and nonhomogeneous MP and SMP.