We study the parametric perturbation of Markov chains with denumerable state spaces. We consider both regular and singular perturbations. By the latter wemean that transition probabilities of aMarkov chain, with several ergodic classes, are perturbed such that (rare) transitions among the different ergodic classes of the unperturbed chain are allowed. Singularly perturbed Markov chains have bee...

Simulation plays an important r^ ole in stochastic geometry and related elds, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium distribution of a Markov chain such as a spatial birth-and-death process. The samples usually fail to be exact...

Human can obtain 3D percept from 2D images on the retinas. However, the neural mechanism of biological stereo vision is largely unknown. On the other hand, Markov random field and belief propagation algorithm have given birth to stereo algorithms with top performance. I propose that brain may employ similar neural network to perceive depth. I design a model combining Markov network with known p...

In many chronic conditions, subjects alternate between an active and an inactive state, and sojourns into the active state may involve multiple lesions, infections, or other recurrences with different times of onset and resolution. We present a biologically interpretable model of such chronic recurrent conditions based on a queueing process. The model has a birth-death process describing recurr...

This paper studies a multi-server queueing system with multiple types of customers and last-come-®rst-served (LCFS) non-preemptive service discipline. First, a quasi-birth-and-death (QBD) Markov process with a tree structure is de®ned and some classical results of QBD Markov processes are generalized. Second, the MMAP[K]/PH[K]/N/LCFS non-preemptive queue is introduced. Using results of the QBD ...

Since the appearance of a paper by Carleial and Hellman [2] in 1975, it is known that the bistable behavior of the ALOHA system is associated with a bimodal shape of the backlog steady-state disbibution. In this paper, we generalize the problem and ask under what conditions a one-dimensional Markov Chain possesses a multimodal steady-state distribution. We restrict our analysis to wtiformly bou...

In this paper we propose a novel MATLAB tool, called Q-MAM, to compute queue length, waiting time and sojourn time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1and GI/M/1-type, quasi-birth-death and non-skip-free Markov chains (implemented by the SMCSolver tool), as well as Markov ...

due to the effective role of markov models in customer relationship management (crm), there is a lack of comprehensive literature review which contains all related literatures. in this paper the focus is on academic databases to find all the articles that had been published in 2011 and earlier. one hundred articles were identified and reviewed to find direct relevance for applying markov models...

Growing amount of information on biological sequences has made application of statistical approaches necessary for modeling and estimation of their functions. In this paper, sensitivity and specificity of the first and second Markov chains for prediction of genes was evaluated using the complete double stranded  DNA virus. There were two approaches for prediction of each Markov Model parameter,...

  In this paper Semi-Markov models are used to forecast the triple dimensions of next earthquake occurrences. Each earthquake can be investigated in three dimensions including temporal, spatial and magnitude. Semi-Markov models can be used for earthquake forecasting in each arbitrary area and each area can be divided into several zones. In Semi-Markov models each zone can be considered as a sta...