This paper mainly analyzes the applications of the Generator matrices in a Continuous Time Markov Chain (CTMC). Hidden Markov models [HMMs] together with related probabilistic models such as Stochastic Context-Free Grammars [SCFGs] are the basis of many algorithms for the analysis of biological sequences. Combined with the continuous-time Markov chain theory of likelihood based phylogeny, stoch...

Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC is needed for some standard distributions, in particular most distributions with regions of zero density such as uniform or shifted distributions. Addressing...

The technique presented in this paper allows the automatic construction of a lumped Markov chain for almost symmetrical Stochastic Well-formed Net (SWN) models. The starting point is the Extended Symbolic Reachability Graph (ESRG), which is a reduced representation of a SWN model reachability graph (RG), based on the aggregation of states into classes. These classes may be used as aggregates fo...

This paper considers a nonstationary multiserver queuing model with abandonment and balking for inbound call centers. We present a continuous time Markov chain (CTMC) model which captures the important characteristics of an inbound call center and obtain a numerical solution for its transient state probabilities using uniformization method with steady-state detection.

Cognitive radio (CR) is an exciting technology to solve the spectrum scarcity problem in future cellular networks. As grade-of-service (GoS) performances directly reflect user's experiences cognitive networks (CCNs), GoS performance analysis of OSA scheme CCNs has attracted much attention. In this article, we derive metrics with a three-dimension continuous-time Markov chain (CTMC) model opport...

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of ...

This letter proposes a simple but accurate approximation to analytically model both the inter-Wireless Local Area Networks (WLANs) interactions and the negative effect of collisions in the performance of high density WLAN scenarios. Inter-WLANs interactions are characterized using a continuous time Markov chain (CTMC) model where states represent the set of active WLANs at a given time. Then, t...

Multistate models characterize disease processes within an individual. Clinical studies often observe the disease status of individuals at discrete time points, making exact times of transitions between disease states unknown. Such panel data pose considerable modeling challenges. Assuming the disease process progresses accordingly, a standard continuous-time Markov chain (CTMC) yields tractabl...

Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), be...

Consider an inventoried item for which reduction in sales price is declared as the age of increases. Decision to maintain at same level/reduce, taken stages 2, · , k − 1, k. On items attaining CLT, they are sold scrap value, provided still left stock. Customer arrival forms a non-homogenous Poisson process, with rate increasing each reduction. Service time follows exponential distribution.The r...