Abstract: In this paper, we study the performance of the strong
stability method of the univariate classical risk model. We interest to
the stability bounds established using two approaches. The first based
on the strong stability method developed for a general Markov chains.
The second approach based on the regenerative processes theory . By
adopting an algorithmic procedure, we study the performance of the
stability method in the case of exponential distribution claim amounts.
After presenting numerically and graphically the stability bounds, an
interpretation and comparison of the results have been done.
Abstract: The primary approach for estimating bridge deterioration uses Markov-chain models and regression analysis. Traditional Markov models have problems in estimating the required transition probabilities when a small sample size is used. Often, reliable bridge data have not been taken over large periods, thus large data sets may not be available. This study presents an important change to the traditional approach by using the Small Data Method to estimate transition probabilities. The results illustrate that the Small Data Method and traditional approach both provide similar estimates; however, the former method provides results that are more conservative. That is, Small Data Method provided slightly lower than expected bridge condition ratings compared with the traditional approach. Considering that bridges are critical infrastructures, the Small Data Method, which uses more information and provides more conservative estimates, may be more appropriate when the available sample size is small. In addition, regression analysis was used to calculate bridge deterioration. Condition ratings were determined for bridge groups, and the best regression model was selected for each group. The results obtained were very similar to those obtained when using Markov chains; however, it is desirable to use more data for better results.
Abstract: In this paper we present a novel error model for
packet loss and subsequent error description. The proposed model
simulates the error performance of wireless communication link. The
model is designed as two independent Markov chains, where the first
one is used for packet generation and the second one generates
correctly and incorrectly transmitted bits for received packets from
the first chain. The statistical analyses of real communication on the
wireless link are used for determination of model-s parameters. Using
the obtained parameters and the implementation of the generator, we
collected generated traffic. The obtained results generated by
proposed model are compared with the real data collection.
Abstract: We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.
Abstract: In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied
Abstract: In this paper we consider a one-dimensional random
geometric graph process with the inter-nodal gaps evolving according
to an exponential AR(1) process. The transition probability matrix
and stationary distribution are derived for the Markov chains concerning
connectivity and the number of components. We analyze the
algorithm for hitting time regarding disconnectivity. In addition to
dynamical properties, we also study topological properties for static
snapshots. We obtain the degree distributions as well as asymptotic
precise bounds and strong law of large numbers for connectivity
threshold distance and the largest nearest neighbor distance amongst
others. Both exact results and limit theorems are provided in this
paper.
Abstract: Most of the real queuing systems include special properties and constraints, which can not be analyzed directly by using the results of solved classical queuing models. Lack of Markov chains features, unexponential patterns and service constraints, are the mentioned conditions. This paper represents an applied general algorithm for analysis and optimizing the queuing systems. The algorithm stages are described through a real case study. It is consisted of an almost completed non-Markov system with limited number of customers and capacities as well as lots of common exception of real queuing networks. Simulation is used for optimizing this system. So introduced stages over the following article include primary modeling, determining queuing system kinds, index defining, statistical analysis and goodness of fit test, validation of model and optimizing methods of system with simulation.
Abstract: Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.
Abstract: The least mean square (LMS) algorithmis one of the
most well-known algorithms for mobile communication systems
due to its implementation simplicity. However, the main limitation
is its relatively slow convergence rate. In this paper, a booster
using the concept of Markov chains is proposed to speed up the
convergence rate of LMS algorithms. The nature of Markov
chains makes it possible to exploit the past information in the
updating process. Moreover, since the transition matrix has a
smaller variance than that of the weight itself by the central limit
theorem, the weight transition matrix converges faster than the
weight itself. Accordingly, the proposed Markov-chain based
booster thus has the ability to track variations in signal
characteristics, and meanwhile, it can accelerate the rate of
convergence for LMS algorithms. Simulation results show that the
LMS algorithm can effectively increase the convergence rate and
meantime further approach the Wiener solution, if the
Markov-chain based booster is applied. The mean square error is
also remarkably reduced, while the convergence rate is improved.