Abstract: This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system length as well as some performance measures at random epochs by using the supplementary variable method. Thirdly, still based on the supplementary variable method we give the probability generating function (PGF) of the number of customers at the beginning of a busy period and give a stochastic decomposition formulae for the PGF of the stationary system length at the departure epochs. Additionally, we investigate the relation between our discretetime system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.
Abstract: Modeling the behavior of the dialogue management in
the design of a spoken dialogue system using statistical methodologies
is currently a growing research area. This paper presents a work
on developing an adaptive learning approach to optimize dialogue
strategy. At the core of our system is a method formalizing dialogue
management as a sequential decision making under uncertainty whose
underlying probabilistic structure has a Markov Chain. Researchers
have mostly focused on model-free algorithms for automating the
design of dialogue management using machine learning techniques
such as reinforcement learning. But in model-free algorithms there
exist a dilemma in engaging the type of exploration versus exploitation.
Hence we present a model-based online policy learning
algorithm using interconnected learning automata for optimizing
dialogue strategy. The proposed algorithm is capable of deriving
an optimal policy that prescribes what action should be taken in
various states of conversation so as to maximize the expected total
reward to attain the goal and incorporates good exploration and
exploitation in its updates to improve the naturalness of humancomputer
interaction. We test the proposed approach using the most
sophisticated evaluation framework PARADISE for accessing to the
railway information system.
Abstract: The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.
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: Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method has often been employed in hierarchical data analysis. In these cases, although the Markov Chain Monte Carlo (MCMC) method is a rather powerful tool for parameter estimation, Procedures regarding MCMC have not been formulated for MHLM. For this reason, this research presents concrete procedures for parameter estimation through the use of the Gibbs samplers. Lastly, several future topics for the use of MCMC approach for HLM is discussed.
Abstract: Next Generation Wireless Network (NGWN) is
expected to be a heterogeneous network which integrates all different
Radio Access Technologies (RATs) through a common platform. A
major challenge is how to allocate users to the most suitable RAT for
them. An optimized solution can lead to maximize the efficient use
of radio resources, achieve better performance for service providers
and provide Quality of Service (QoS) with low costs to users.
Currently, Radio Resource Management (RRM) is implemented
efficiently for the RAT that it was developed. However, it is not
suitable for a heterogeneous network. Common RRM (CRRM) was
proposed to manage radio resource utilization in the heterogeneous
network. This paper presents a user level Markov model for a three
co-located RAT networks. The load-balancing based and service
based CRRM algorithms have been studied using the presented
Markov model. A comparison for the performance of load-balancing
based and service based CRRM algorithms is studied in terms of
traffic distribution, new call blocking probability, vertical handover
(VHO) call dropping probability and throughput.
Abstract: In most study fields, a phenomenon may not be
studied directly but it will be examined indirectly by phenomenon
model. Making an accurate model of system, there is attained new
information from modeled phenomenon without any charge, danger,
etc... there have been developed more solutions for describing and
analyzing the recent complicated systems but few of them have
analyzed the performance in the range of system description. Petri
nets are of limited solutions which may make such union. Petri nets
are being applied in problems related to modeling and designing the
systems. Theory of Petri nets allow a system to model
mathematically by a Petri net and analyzing the Petri net can then
determine main information of modeled system-s structure and
dynamic. This information can be used for assessing the performance
of systems and suggesting corrections in the system. In this paper,
beside the introduction of Petri nets, a real case study will be studied
in order to show the application of generalized stochastic Petri nets in
modeling a resource sharing production system and evaluating the
efficiency of its machines and robots. The modeling tool used here is
SHARP software which calculates specific indicators helping to
make decision.
Abstract: Quantitative trait loci (QTL) experiments have yielded
important biological and biochemical information necessary for
understanding the relationship between genetic markers and
quantitative traits. For many years, most QTL algorithms only
allowed one observation per genotype. Recently, there has been an
increasing demand for QTL algorithms that can accommodate more
than one observation per genotypic distribution. The Bayesian
hierarchical model is very flexible and can easily incorporate this
information into the model. Herein a methodology is presented that
uses a Bayesian hierarchical model to capture the complexity of the
data. Furthermore, the Markov chain Monte Carlo model composition
(MC3) algorithm is used to search and identify important markers. An
extensive simulation study illustrates that the method captures the
true QTL, even under nonnormal noise and up to 6 QTL.
Abstract: Using Dynamic Bayesian Networks (DBN) to model genetic regulatory networks from gene expression data is one of the major paradigms for inferring the interactions among genes. Averaging a collection of models for predicting network is desired, rather than relying on a single high scoring model. In this paper, two kinds of model searching approaches are compared, which are Greedy hill-climbing Search with Restarts (GSR) and Markov Chain Monte Carlo (MCMC) methods. The GSR is preferred in many papers, but there is no such comparison study about which one is better for DBN models. Different types of experiments have been carried out to try to give a benchmark test to these approaches. Our experimental results demonstrated that on average the MCMC methods outperform the GSR in accuracy of predicted network, and having the comparable performance in time efficiency. By proposing the different variations of MCMC and employing simulated annealing strategy, the MCMC methods become more efficient and stable. Apart from comparisons between these approaches, another objective of this study is to investigate the feasibility of using DBN modeling approaches for inferring gene networks from few snapshots of high dimensional gene profiles. Through synthetic data experiments as well as systematic data experiments, the experimental results revealed how the performances of these approaches can be influenced as the target gene network varies in the network size, data size, as well as system complexity.
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: Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.
Abstract: In this paper we present a novel approach for human
Body configuration based on the Silhouette. We propose to address
this problem under the Bayesian framework. We use an effective
Model based MCMC (Markov Chain Monte Carlo) method to solve
the configuration problem, in which the best configuration could be
defined as MAP (maximize a posteriori probability) in Bayesian
model. This model based MCMC utilizes the human body model to
drive the MCMC sampling from the solution space. It converses the
original high dimension space into a restricted sub-space constructed
by the human model and uses a hybrid sampling algorithm. We
choose an explicit human model and carefully select the likelihood
functions to represent the best configuration solution. The
experiments show that this method could get an accurate
configuration and timesaving for different human from multi-views.
Abstract: In this paper we investigate the influence of external
noise on the inference of network structures. The purpose of our
simulations is to gain insights in the experimental design of microarray
experiments to infer, e.g., transcription regulatory networks
from microarray experiments. Here external noise means, that the
dynamics of the system under investigation, e.g., temporal changes of
mRNA concentration, is affected by measurement errors. Additionally
to external noise another problem occurs in the context of microarray
experiments. Practically, it is not possible to monitor the mRNA
concentration over an arbitrary long time period as demanded by the
statistical methods used to learn the underlying network structure. For
this reason, we use only short time series to make our simulations
more biologically plausible.
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: This paper presents a novel method for remaining
useful life prediction using the Elliptical Basis Function (EBF)
network and a Markov chain. The EBF structure is trained by a
modified Expectation-Maximization (EM) algorithm in order to take
into account the missing covariate set. No explicit extrapolation is
needed for internal covariates while a Markov chain is constructed to
represent the evolution of external covariates in the study. The
estimated external and the unknown internal covariates constitute an
incomplete covariate set which are then used and analyzed by the EBF
network to provide survival information of the asset. It is shown in the
case study that the method slightly underestimates the remaining
useful life of an asset which is a desirable result for early maintenance
decision and resource planning.
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: In unsupervised segmentation context, we propose a bi-dimensional hidden Markov chain model (X,Y) that we adapt to the image segmentation problem. The bi-dimensional observed process Y = (Y 1, Y 2) is such that Y 1 represents the noisy image and Y 2 represents a noisy supplementary information on the image, for example a noisy proportion of pixels of the same type in a neighborhood of the current pixel. The proposed model can be seen as a competitive alternative to the Hilbert-Peano scan. We propose a bayesian algorithm to estimate parameters of the considered model. The performance of this algorithm is globally favorable, compared to the bi-dimensional EM algorithm through numerical and visual data.
Abstract: C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.
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.