This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth–death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman–Kolmogorov differential equations are developed with the use of mnemonic rule and these equation...

Bayesian total-evidence dating involves the simultaneous analysis of morphological data from the fossil record and morphological and sequence data from recent organisms, and it accommodates the uncertainty in the placement of fossils while dating the phylogenetic tree. Due to the flexibility of the Bayesian approach, total-evidence dating can also incorporate additional sources of information. ...

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural mo...

In this article, we investigate the MEMM (Minimal relative Entropy Martingale Measure) of Birth and Death processes and the MEMM of generalized Birth and Death processes. We see that the existence problem of the MEMM is reduced to the problem of solving the corresponding Hamilton-Jacobi-Bellman equation.

We consider birth-death processes taking values in N ≡ {0, 1, . . .}, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions {pij(t)} and {p̃ij(t)} are said to be similar if, for all i, j ∈ N , there are constants cij such that p̃ij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a b...

We present an efficient, reliable, and easy-to-implement algorithm to compute steady-state probabilities for birth-death processes whose upper-tail probabilities decay geometrically or faster. The algorithm can provide any required accuracy and it avoids overand underflow. In addition to steady-state probabilities, the algorithm can compute any performance measure that can be expressed as the e...

We consider a birth-death process with the birth rates iλ and death rates iμ+i(i−1)θ, where i is the current state of the process. A positive competition rate θ is assumed to be small. In the supercritical case when λ > μ this process can be viewed as a demographic model for a population with a high carrying capacity around λ−μ θ . The article reports in a self-contained manner on the asymptoti...

In this paper, we study a birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems ...

First, we revisit a classic two-type branching process which describes cell proliferation and mutation; widespread application has been seen in cancer and microbial modelling. As the mutation rate tends to zero and the population size to infinity, the mutation times converge to a Poisson process. This yields the number of mutants and clone sizes. Other limits and exact results are also explored...