Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 11

Markov Chain Related Publications

11 Stability Bound of Ruin Probability in a Reduced Two-Dimensional Risk Model

Authors: Zina Benouaret, Djamil Aissani

Abstract:

In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov Chain, risk models, ruin probabilities, strong stability analysis

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10 Performance of the Strong Stability Method in the Univariate Classical Risk Model

Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani

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.

Keywords: Markov Chain, ruin probability, risk models, strong stability, regenerative processes

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9 Markov Chain Based QoS Support for Wireless Body Area Network Communication in Health Monitoring Services

Authors: R. A. Isabel, E. Baburaj

Abstract:

Wireless Body Area Networks (WBANs) are essential for real-time health monitoring of patients and in diagnosing of many diseases. WBANs comprise many sensors to monitor a large range of ambient conditions. Quality of Service (QoS) is a key challenge in WBAN, because the different state information of the neighboring nodes has to be monitored in an accurate manner. However, energy consumption gets increased while predicting and maintaining the exact information in highly dynamic environments. In order to reduce energy consumption and end to end delay, Markov Chain Based Quality of Service Support (MC-QoSS) method is designed in the health monitoring services of WBAN communication. The energy consumption gets reduced by forming a Markov chain with high energy nodes in the sensor networks communication path. The low energy level sensor nodes are removed using transitional probability in order to reduce end to end delay. High energy nodes are formed in the chain structure of its corresponding path to enhance communication. After choosing the communication path through high energy nodes, the packets are sent to the sink node from the source node with a higher Packet Delivery Ratio. The simulation result shows that MC-QoSS method improves the packet delivery ratio and reduces energy consumption with minimum end to end delay, compared to existing methods.

Keywords: quality of service, Markov Chain, Wireless Body Area Networks, health monitoring services

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8 Budget Optimization for Maintenance of Bridges in Egypt

Authors: Sherif M. Hafez, Hesham Abd Elkhalek, Yasser M. El Fahham

Abstract:

Allocating limited budget to maintain bridge networks and selecting effective maintenance strategies for each bridge represent challenging tasks for maintenance managers and decision makers. In Egypt, bridges are continuously deteriorating. In many cases, maintenance works are performed due to user complaints. The objective of this paper is to develop a practical and reliable framework to manage the maintenance, repair, and rehabilitation (MR&R) activities of Bridges network considering performance and budget limits. The model solves an optimization problem that maximizes the average condition of the entire network given the limited available budget using Genetic Algorithm (GA). The framework contains bridge inventory, condition assessment, repair cost calculation, deterioration prediction, and maintenance optimization. The developed model takes into account multiple parameters including serviceability requirements, budget allocation, element importance on structural safety and serviceability, bridge impact on network, and traffic. A questionnaire is conducted to complete the research scope. The proposed model is implemented in software, which provides a friendly user interface. The framework provides a multi-year maintenance plan for the entire network for up to five years. A case study of ten bridges is presented to validate and test the proposed model with data collected from Transportation Authorities in Egypt. Different scenarios are presented. The results are reasonable, feasible and within acceptable domain.

Keywords: Markov Chain, bridge management systems (BMS), cost optimization condition assessment, fund allocation

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7 Application of Finite Dynamic Programming to Decision Making in the Use of Industrial Residual Water Treatment Plants

Authors: Oscar Vega Camacho, Andrea Vargas Guevara, Ellery Rowina Ariza

Abstract:

This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its wastewater treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: Decision Making, Optimization, wastewater, Markov Chain

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6 A Generator from Cascade Markov Model for Packet Loss and Subsequent Bit Error Description

Authors: Jaroslav Polec, Michal Martinovič, Kvetoslava Kotuliaková, Viliam Hirner

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.

Keywords: generator, Wireless Channel, Markov Chain, IEEE 802.11, error model, Elliot model, Gilbert model

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5 Remaining Useful Life Prediction Using Elliptical Basis Function Network and Markov Chain

Authors: Yi Yu, Lin Ma, Yong Sun, Yuantong Gu

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.

Keywords: Markov Chain, Remaining Useful Life, Elliptical Basis Function Network, Missing Covariates

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4 A Novel Convergence Accelerator for the LMS Adaptive Algorithm

Authors: Jeng-Shin Sheu, Jenn-Kaie Lain, Tai-Kuo Woo, Jyh-Horng Wen

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.

Keywords: Markov Chain, LMS, accelerator, convergence rate

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3 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching

Authors: Shouming Zhong, Xia Zhou

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.

Keywords: Synchronization, Markov Chain, Brownian motion, M-matrix, delay-range-dependent, generalized Itō's formula

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2 Application of Generalized Stochastic Petri Nets(GSPN) in Modeling and Evaluating a Resource Sharing Flexible Manufacturing System

Authors: Aryanejad Mir Bahador Goli, Zahra Honarmand Shah Zileh

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.

Keywords: Performance Evaluation, Markov Chain, flexible manufacturing system, generalizedstochastic Petri nets

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1 A Markov Chain Approximation for ATS Modeling for the Variable Sampling Interval CCC Control Charts

Authors: C. Y. Chen, Y. K. Chen, K. C. Chiou

Abstract:

The cumulative conformance count (CCC) charts are widespread in process monitoring of high-yield manufacturing. Recently, it is found the use of variable sampling interval (VSI) scheme could further enhance the efficiency of the standard CCC charts. The average time to signal (ATS) a shift in defect rate has become traditional measure of efficiency of a chart with the VSI scheme. Determining the ATS is frequently a difficult and tedious task. A simple method based on a finite Markov Chain approach for modeling the ATS is developed. In addition, numerical results are given.

Keywords: Markov Chain, control chart, average time to signal, Cumulative conformance count, variable sampling interval

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