In this paper, we are concerned with a time-inhomogeneous version of the Markovian Arrival Process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resul...

In this paper, we introduce a Bayesian analysis for non-homogeneous Poisson process in software reliability models. Posterior summaries of interest are obtained using Markov chain Monte Carlo methods. We compare the results obtained from using conjugate and reference priors. Model selection based on the prequential conditional predictive ordinates is developed.

A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficien...

Manpower Planning is the prerequisite for efficient management of any organization. The stability of the graded structure in corporate and government offices plays a dominant role for efficient planning and control of human resources. The constituent components of a manpower planning model are recruitment process, promotion process and leaving process. This paper addresses a two-graded manpower...

The process obtained by rescaling a homogeneous Poisson process by the maximum likelihood estimate of its intensity is shown to have surprisingly strong self-correcting behavior. Formulas for the conditional intensity and moments of the rescaled Poisson process are derived, and its behavior is demonstrated using simulations. Relationships to the Brownian Bridge are explored, and implications fo...

In this paper we present various approaches for the transient analysis of a Markovian population process with total catastrophes. We discuss the pros and the cons of these methodologies and point out how they lead to different tractable extensions. As an illustrating example, we consider the non-homogeneous Poisson process with total catastrophes. The extension of the probabilistic methodologie...

Precipitation has a dominant role in agriculture, and regular rain pattern is usually vital to agriculture; excessive or inadequate rainfall can be harmful. In this paper, an agricultural drought index utilized study the periods analyze them with their intensities at various locations. Some nonhomogeneous Poisson models are also used calculate probability of droughts (number times occurred) tim...