Markov Chain Approach Research Articles

How the COVID-19 Pandemic Affected Developing Countries: the Tunisian Investigation

The consequences of COVID-19 vary considerably from country to country and from sector to sector. In this paper, we examine how employment in sectors of Tunisian economy is being affected by the COVID-19 pandemic. For this purpose, we apply the Markov chain approach. This method has the merit to model a system that changes states according to a transition rule that depends only on the current state. We find that the COVID-19 have a negative impact on the employment in industry and in service. Moreover, the agricultural sector benefits most from COVID-19. It is important to plan for economic measures in order to support the resilience of economic establishments, particularly small- and medium-sized enterprises.

A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements.

In this paper, we consider a periodic-review stochastic inventory system with both minimum and maximum order quantity (MinOQ and MaxOQ, respectively) requirements. In each period, if an order is placed, the order quantity is bounded, at least at the MinOQ and at most the MaxOQ. The optimal policy of such a system is unknown, and even if it exists, it must be quite complicated. We propose a heuristic policy, called the modified (s, S) policy, under which whenever the inventory position drops to the reorder point s or below, an order is placed to raise the inventory position as close as possible to the order-up-to level S. Applying a discrete-time Markov chain approach, we are able to compute the system-wide long-run average cost. We provide bounds for the optimal values of s and S and design an efficient algorithm to optimize our proposed policy. In addition, the proposed heuristic policy has excellent performance in our numerical studies. We also measure the impact of some inventory parameters.Supplementary InformationThe online version supplementary material available at 10.1007/s10479-021-04441-1.

Short Words Signature Verification using Markov Chain and Fisher Linear Discriminant Approach

Short Words Signature Verification using Markov Chain and Fisher Linear Discriminant Approach

A queuing network and Markov chain approach for balancing assembly line: A case study

A queuing network and Markov chain approach for balancing assembly line: A case study

Anomaly Detection for Compositional Data using VSI MEWMA control chart

In recent years, the monitoring of compositional data using control charts has been investigated in the Statistical Process Control field. In this study, we will design a Phase II Multivariate Exponentially Weighted Moving Average (MEWMA) control chart with variable sampling intervals to monitor compositional data based on isometric log-ratio transformation. The Average Time to Signal will be computed based on the Markov chain approach to investigate the performance of the proposed chart. We also propose an optimization procedure to obtain the optimal control limit, smoothing constant, and out-of-control Average Time to Signal for different shift sizes and short sampling intervals. The performance of the proposed chart in comparison with the standard MEWMA chart for monitoring compositional data is also provided. Finally, we end the paper with a conclusion and some recommendations for future research.

A queuing network and Markov chain approach for balancing assembly line: a case study

A queuing network and Markov chain approach for balancing assembly line: a case study

A Markov Chain Approach for Myopic Multi-Hop Relaying: Outage and Diversity Analysis

In this paper, a cooperative protocol is investigated for a multi-hop network consisting of relays with buffers of finite size, which may operate in different communication modes. The protocol is based on the myopic decode-and-forward strategy, where each node of the network cooperates with a limited number of neighboring nodes for the transmission of the signals. Each relay stores in its buffer the messages that were successfully decoded, in order to forward them through the appropriate channel links, based on its supported communication modes. A complete theoretical framework is investigated that models the evolution of the buffers and the transitions at the operations of each relay as a state Markov chain (MC). We analyze the performance of the proposed protocol in terms of outage probability and derive an expression for the achieved diversity-multiplexing tradeoff, by using the state transition matrix and the related steady state of the MC. Our results show that the proposed protocol outperforms the conventional multi-hop relaying scheme and the system's outage probability as well as the achieved diversity order depend on the degree of cooperation among neighboring nodes and the communication model that is considered for every relay of the network.

Energy Resilience Impact of Supply Chain Network Disruption to Military Microgrids

The ability to provide uninterrupted power to military installations is paramount in executing a country’s national defense strategy. Microgrid architectures increase installation energy resilience through redundant local generation sources and the capability for grid independence. However, deliberate attacks from near-peer competitors can disrupt the associated supply chain network, thereby affecting mission critical loads. Utilizing an integrated discrete-time Markov chain and dynamic Bayesian network approach, we investigate disruption propagation throughout a supply chain network and quantify its mission impact on an islanded microgrid. We propose a novel methodology and an associated metric we term “energy resilience impact” to identify and address supply chain disruption risks to energy security. The proposed methodology addresses a gap in the literature and practice where it is assumed supply chains will not be disrupted during incidents involving microgrids. A case study of a fictional military installation is presented to demonstrate how installation energy managers can adopt this methodology for the design and improvement of military microgrids. The fictional case study shows how supply chain disruptions can impact the ability of a microgrid to successfully supply electricity to critical loads throughout an islanding event.

Impact of Land Use and Climate Changes on Flood Inundation Areas in the Lower Cimanuk Watershed, West Java Province

Land use and climatic changes potentially affect the surface runoff and inundation in watershed zones. Every year, the outflow of the Cimanuk River causes floods across the majority of the upper area of the Cimanuk Watershed, as well as the lower area. This study aimed to assess the impact of climatic and land use changes on future flood inundation in the Lower Cimanuk Watershed using a RRI model. Land-use change has been prepared by modeling using a multi-layer perceptron neural network and Markov Chain approach, while climate change using HadGEM2-ES global climate model data under scenarios RCP4.5. In particular, the forest area was projected to decline in this watershed zone, from 19.54% of the total area in 2019 to 17.73% in 2050. Similarly, the area of paddy fields was predicted to decline from approximately 34.36% in 2019 to 29.65% in 2050. In contrast, other types of land use such as dryland agriculture, mixed dryland agriculture, and settlements were projected to increase in the future. The coverage of the simulated flood inundation area using the Rainfall-Runoff Inundation model estimated to reach 179.4 km2 in 2019. The simulation results showed an increase in flood inundation areas in 2030 and 2050, alongside changes in land use and climate. The areas affected by flood inundation were estimated to reach 253.3 km2in 2030. This coverage was expected to increase by 311.9 km2 in 2050, with severely affected land uses including settlements, dry land agriculture, mixed dry land agriculture, paddy fields, and ponds.

The combined Shewhart-CUSUM sign charts

A Shewhart control chart is highly effective for detecting large process shifts, however, it is relatively less sensitive to the small shifts. A CUSUM chart is more efficient than a Shewhart chart for detecting small process shifts but it is inferior to that for detecting the large ones. This paper proposes the nonparametric combined Shewhart-CUSUM (CSC) control charts based on the sign statistic. By appropriately choosing the design parameters, a CSC chart exhibits a trade-off statistical performance between that of the Shewhart and CUSUM sign charts. That is, its performance lies between the performances of the Shewhart and CUSUM sign charts for detecting a process shift of any size. The expressions for the zero-state and steady-state average run lengths of the CSC chart are obtained using a Markov chain approach. An example illustrating the implementation of this chart is provided.

Mathematical Modeling of Manufacturing Lines with Distribution by Process: A Markov Chain Approach

Today, there are a wide variety of ways to produce goods in a manufacturing company. Among the most common are mass or line production and process production, both of which are antagonists. In an online production system, materials move from station to station, receiving added value on a well-defined layout. In a production line by process, the materials randomly visit a set of machines strategically located in order to receive a treatment, almost always through metalwork machines, according to the final product of which they will be part. In this case, there is not a predefined layout, as the incoming materials are sectioned and each piece forms a continuous flow through different workstations to receive some process. This activity depends on the function of the product and its final destination as a component of a finished product. In this proposal, Markov chain theory is used to model a manufacturing system by process in order to obtain the expected values of the average production per machine, the total expected production in all the facilities, the leisure per machine and the total productive efficiency of the system, among other indicators. In this research, we assume the existence of historical information about the use of the equipment, its failures, the causes of failure and their repair times; in any factory, this information is available in the area of manufacturing engineering and plant engineering. From this information, statistical frequency indicators are constructed to estimate transition probabilities, from which the results presented here are derived. The proposal is complemented with a numerical example of a real case obtained from a refrigerator factory established in Mexico in order to illustrate the results derived from this research. The results obtained show their feasibility when successfully implemented in the company.

The SPRT control charts for the Maxwell distribution

AbstractMaxwell distribution has several applications in modeling physical and chemical processes, as well as in reliability and lifetime data analysis. In this paper, we propose the one‐ and two‐sided SPRT control charts for monitoring the scale parameter of a Maxwell distributed process. Using a Markov chain approach, we obtain the measures of statistical performance for the one‐sided charts. Reasonably accurate relationships between the performance measures of a two‐sided SPRT chart and that of its corresponding one‐sided charts are derived through Monte‐Carlo simulations. Approaches for designing the one‐ and two‐sided SPRT charts having the specified in‐control and the optimal out‐of‐control performances are provided. The results of the numerical study reveal that the proposed charts significantly outperform the Shewhart and cumulative sum (CUSUM) charts for detecting a shift of any size in the scale parameter. The mechanisms of the one‐ and two‐sided SPRT charts are illustrated via two real‐data examples: the first in the monitoring of the urinary glycosaminoglycan concentration and the second in the monitoring of the bearing life.

Markovian approach to tackle competing pathogens in simplicial complex

Recent studies on network spreading dynamics often adopt pairwise interaction to describe the simple spreading process while using higher-order interaction to describe the collective behavior of the dynamical system on the network. However, the interaction between competing pathogens usually includes both pairwise and high-order interactions. Due to dynamic correlation, it is hard to solve the theory by considering two modes of interaction. Here, we propose a theoretical analysis framework based on Microscopic Markov Chain Approach (MMCA) to solve simplicial competing spreading involving pairwise and high-order interactions. Because of the competitive mechanism in the framework, a susceptible node can only be infected by one pathogen, and contagion can spread simultaneously through pairwise interactions (1-simplices) and higher-order interactions, i.e., 2-simplices. The theory and simulation agree in good accuracy on real networks and artificial networks, which reveals the validity of the theoretical analysis and indicates that the initial density of the two pathogens and the infection rate of 1-simplices act together on the process of pathogen transmission. The effect of 1-simplices and 2-simplices infection rates of two pathogens are also included in the discussion. When the average degree of the network is fixed, in the case of a larger average number of 1-simplices incidents on a node, infection rates of pathogen A is greater than infection rates of pathogen B may result in final infection density of pathogen A greater than the final infection density of pathogen B. We discuss the influences of 1-simplices average degree and 2-simplices average degree on the final infection range. We find that with the increase of 1-simplices average degree, the pathogen may undergo a transition from outbreak to death while increasing the 2-simplices average degree is more conducive to spreading. Finally, in the study of two different seed selection strategies, we find that selecting the nodes with the highest degree as seeds can promote pathogen spreading more than randomly selecting seeds.

A Markov Chain Approach for Myopic Multi-hop Relaying: Outage and Diversity Analysis

A Markov Chain Approach for Myopic Multi-hop Relaying: Outage and Diversity Analysis

Study of spreading phenomenon in network population considering heterogeneous property

In practice, it is well known that the environment plays an essential role in affecting personal opinions regarding epidemics. In this paper, we assume that personal recovery rate from infected state varies and corresponding recovery value is affected by the number of aware and susceptible neighbors while this is referred to as resource for simplicity. A tunable factor, i.e., α, is introduced indicating the rate of resource utilization, while this parameter is adopted to characterize the effect of neighbors to individual’s recovery rate. For simplicity, the UAU-SIS model is adopted to study the spreading phenomenon. Later, extensive Monte Carlo simulations are conducted; for comparison, theoretical results are also derived through microscopic Markov chain approach. Regardless of the considered network topology, we can easily find that the obtained results are consistent from the epidemic level. Furthermore, the fraction of infected individuals or aware individuals seems to increase with the increase of resource utilization rate. This is incurred by the fact that a larger recovery rate will be obtained for higher resource utilization rate. We also devote our efforts deriving the epidemic spreading threshold while the threshold value decreases for larger. Thus, we can conclude that the resource utilization rate plays a negative role in eliminating epidemics. We hope the findings here can contribute the understanding about spreading phenomenon in network population given heterogeneous recovery rate.

Analysis of the tendency of transition between segments of green consumer behavior with a Markov chain approach

PurposeThis study aims to determine the number of segments of green consumer behavior on toiletries products, and the tendency of transition between clusters is estimated. This study also provides recommendations based on the results.Design/methodology/approachThis study used primary data collected through an online and offline questionnaire. The questionnaire was intended to identify the socio-demographic characteristics, green consumer behavior state according to the environment as well as the willingness of the respondents to purchase various toiletries products (current, less green, and greener). Prior to segmenting green consumer behavior, scale purification using confirmatory factor analysis was performed to ensure the indicators used were valid. The k-means clustering algorithm was used for the segmentation, while discriminant analysis was used to validate the segmentation result. The Markov chain approach was performed to estimate the tendency of the transition between constructed segments, where the logistic regression model was applied to predict the individual transition probability.FindingsThe clustering algorithm resulted in three segments: light green, green and dark green. The light green segment has the lowest attitude toward the environmental criteria while the members of the dark green segment have the highest attitude among the other segments. The logistic regression indicated that the tendency of individuals to stay in the current segment or move to the adjacent segment was influenced by socio-demographic factors. The one-step transition probability matrix revealed that the tendency of a particular segment to move to the greener segment was greater than to stay or even move to the less green segment. The Markov chain approach then showed that the steady-state condition will emerge after 18 steps.Research limitations/implicationsThis study was limited geographically and by the criteria used for segmenting the green consumer behavior; therefore, it is recommended that this study be replicated on a greater scale with more criteria. A wider geographic area could be considered, including a national study, and more criteria, such as social influences, could be considered. This study does not focus on specific toiletries products. Selecting more specific toiletries products could be considered to provide a more reliable response from the respondents. Moreover, factors around the willingness to pay for green products were not investigated in greater detail although these factors might become indicators that can distinguish between two or more segments.Practical implicationsThis study empirically supports the theory that consumer environmentally friendly behavior can be used to appropriately categorize consumers into several segments, and thereby guide the development of a more differentiated policy approach for business and government.Social implicationsGreen consumer behavior may help save the environment and it will be beneficial in reducing environmental damage.Originality/valueThe study extends the existing literature related to green consumer behavior by segmenting the green consumer behavior based on the environmental criteria and applying the Markov chain approach to estimate the tendency of transition between segments.

The dynamic interdependence in the demand of primary and emergency secondary care: A hidden Markov approach

SummaryThis paper develops an extension of the class of finite mixture models for longitudinal count data to the bivariate case by using a hidden Markov chain approach. The model allows for disentangling unobservable time‐varying heterogeneity from the dynamic effect of utilisation of primary and secondary care and measuring their potential substitution effect. Three points of supports adequately describe the distribution of the latent states suggesting the existence of three profiles of low, medium and high users who shows persistency in their behaviour, but not permanence as some switch to their neighbour's profile.

Structural Change Analysis of Groundnut Export Markets of India: Markov Chain Approach

Structural Change Analysis of Groundnut Export Markets of India: Markov Chain Approach

Fast Sampling and Counting k -SAT Solutions in the Local Lemma Regime

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k -uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd < n o(1) and k ≥ 20 log k + 20 log d + 60, the new sampling algorithm runs in close to linear time, and the counting algorithm runs in close to quadratic time. Our approach is inspired by Moitra (JACM, 2019), which remarkably utilizes the Lovász local lemma in approximate counting. Our main technical contribution is to use the local lemma to bypass the connectivity barrier in traditional Markov chain approaches, which makes the well-developed MCMC method applicable on disconnected state spaces such as SAT solutions. The benefit of our approach is to avoid the enumeration of local structures and obtain fixed polynomial running times, even if k = ω (1) or d = ω (1).

A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this work, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.