Steady-state Probability Research Articles

Spatiotemporal analysis of meteorological drought variability in a homogeneous region using standardized drought indices

Drought is one of the most common climatic or meteorological hazards and has spatiotemporal characteristics that substantially impact the livelihoods and economy worldwide. Therefore, there is a need for efficient procedures that accurately identify spatiotemporal variability. Moreover, it is crucial to continuously assess and monitor spatiotemporal drought occurrence in a certain region to prevent unfavourable impacts. For this purpose, the current study develops a new procedure for spatiotemporal analysis of the region: The Spatio-Temporal Weighted Joint Agglomerative Drought Index (STWJADI). The STWJADI is mainly based on a weighting scheme known as the Spatio-Temporal Two-Stage Standardized Weighting Scheme (STTSSWS). In the first stage of the STTSSWS, the steady-state probabilities are computed for several stations (Astor, Bunji, Chilas, Gupis, Skardu, and Gilgit) of the Northern region of Pakistan at a 1-month time scale (scale-1) to allocate weights for various drought classes. Moreover, in the second stage of the STTSSWS, the weights are allocated based on spatiotemporal weighting characteristics to acquire new weights for the numerous drought classes in the designated region. Further, the spatiotemporal weights attained from STTSSWS are utilized to compute the STWJADI. The outcomes of the STWJADI provide efficient and comprehensive information for drought characterization in the selected region.

Mean-field analysis of Stuart-Landau oscillator networks with symmetric coupling and dynamical noise.

This paper presents analyses of networks composed of homogeneous Stuart-Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.

Vulnerability Analysis of LTE-R Train-to-Ground Communication Time Synchronization

The time synchronization of LTE-R train-to-ground communication systems plays an important role in ensuring the safety of high-speed railways. In the LTE-R time synchronization process, existing problems, such as the time synchronization message broadcast address and LTE-R all-IP architecture, are vulnerable to attack. In order to analyze the impact of these problems, we propose a new vulnerability analysis method of LTE-R time synchronization based on stochastic Petri nets. Firstly, we construct a stochastic Petri net model of an LTE-R time synchronization process under attack. Secondly, steady-state probability expressions are obtained using the model isomorphism Markov chain. Finally, bychanging the firing rate of several key vulnerable nodes, the relationship curve between the firing rate and the steady-state probability of the clock node is obtained. Simulations show that the vulnerability of LTE-R time synchronization is most affected by the attack on eNodeB of the LTE-R base station. The results can provide a certain theoretical basis for the evolution of high-speed railway GSM-R communication systems to LTE-R.

The role of harvesting in population control in the presence of correlated noise sources

In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of correlated noise sources. Our aim is to determine a statistical correlation between the noises in the model parameters and population size. The characteristic time scale over which the population size of prey and predator varies are very much different, this fact justifies to consider a single species model as the predator population can be chosen to be constant within the generation time of prey. Steady state probability distributions and stationary potentials of the population are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant harvesting. One of our key findings is the transition from bistable to tristable state for weak noises. Another valuable finding is the noise enhanced stability phenomenon for negatively correlated noises. Constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case to reduce population size. The obtained results may be helpful to understand toxin producing phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak or extinction in forest.

Lost sales obsolescence inventory systems with positive lead time: a system-point level-crossing approach

AbstractIn this article, we provide a comprehensive analyses of two continuous review lost sales inventory system based on different replenishment policies, namely $(s,S)$ and $(s,Q)$. We assume that the arrival times of demands form a Poisson process and that the demand sizes have i.i.d. exponential distribution. We assume that the items in stock may obsolete after an exponential time. The lead time for replenishment is exponential. We also assume that the excess demands and the demands that occurred during stock out periods are lost. Using the system point method of level crossing and integral equation method, we derive the steady-state probability distribution of inventory level explicitly. After deriving some system performance measures, we computed the total expected cost rate. We also provide numerical examples of sensitivity analyses involving different parameters and costs. As a result of our numerical analysis, we provide several insights on the optimal $(s,S)$ and $(s,Q)$ policies for inventory systems of obsolescence items with positive lead times. The better policy for maintaining inventory can be quantified numerically.

Retrial Queuing-Inventory Systems with Delayed Feedback and Instantaneous Damaging of Items

This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal to zero upon arrival of a primary customer, then this customer, according to the Bernoulli scheme, either leaves the system or goes into an infinite buffer to repeat their request in the future. The rate of retrial customers is constant, and if the inventory level is zero upon arrival of a retrial customer, then this customer, according to the Bernoulli scheme, either leaves orbit or remains in orbit to repeat its request in the future. According to the Bernoulli scheme, each served primary or retrial customer either leaves the system or feedbacks into orbit to repeat their request. Destructive customers that form a Poisson flow cause damage to items. Unlike primary, retrial, and feedback customers, destructive customers do not require items, since, upon arrival of such customers, the inventory level instantly decreases by one. The system adopted one of two replenishment policies: (s, Q) or (s, S). In both policies, the lead time is a random variable that has an exponential distribution. It is shown that the mathematical model of the system under study was a two-dimensional Markov chain with an infinite state space. Algorithms for calculating the elements of the generating matrices of the constructed chains were developed, and the ergodicity conditions for both policies were found. To calculate the steady-state probabilities, a matrix-geometric method was used. Formulas were found for calculating the main performance measures of the system. The results of the numerical experiments, including the minimization of the total cost, are demonstrated.

A new comprehensive approach for regional drought monitoring.

The Standardized Precipitation Index (SPI) is a vital component of meteorological drought. Several researchers have been using SPI in their studies to develop new methodologies for drought assessment, monitoring, and forecasting. However, it is challenging for SPI to provide quick and comprehensive information about precipitation deficits and drought probability in a homogenous environment. This study proposes a Regional Intensive Continuous Drought Probability Monitoring System (RICDPMS) for obtaining quick and comprehensive information regarding the drought probability and the temporal evolution of the droughts at the regional level. The RICDPMS is based on Monte Carlo Feature Selection (MCFS), steady-state probabilities, and copulas functions. The MCFS is used for selecting more important stations for the analysis. The main purpose of employing MCFS in certain stations is to minimize the time and resources. The use of MCSF makes RICDPMS efficient for drought monitoring in the selected region. Further, the steady-state probabilities are used to calculate regional precipitation thresholds for selected drought intensities, and bivariate copulas are used for modeling complicated dependence structures as persisting between precipitation at varying time intervals. The RICDPMS is validated on the data collected from six meteorological locations (stations) of the northern area of Pakistan. It is observed that the RICDPMS can monitor the regional drought and provide a better quantitative way to analyze deficits with varying drought intensities in the region. Further, the RICDPMS may be used for drought monitoring and mitigation policies.

A new spatiotemporal two-stage standardized weighted procedure for regional drought analysis.

Drought is a complex phenomenon that occurs due to insufficient precipitation. It does not have immediate effects, but sustained drought can affect the hydrological, agriculture, economic sectors of the country. Therefore, there is a need for efficient methods and techniques that properly determine drought and its effects. Considering the significance and importance of drought monitoring methodologies, a new drought assessment procedure is proposed in the current study, known as the Maximum Spatio-Temporal Two-Stage Standardized Weighted Index (MSTTSSWI). The proposed MSTTSSWI is based on the weighting scheme, known as the Spatio-Temporal Two-Stage Standardized Weighting Scheme (STTSSWS). The potential of the weighting scheme is based on the Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and the steady-state probabilities. Further, the STTSSWS computes spatiotemporal weights in two stages for various drought categories and stations. In the first stage of the STTSSWS, the SPI, SPEI, and the steady-state probabilities are calculated for each station at a 1-month time scale to assign weights for varying drought categories. However, in the second stage, these weights are further propagated based on spatiotemporal characteristics to obtain new weights for the various drought categories in the selected region. The STTSSWS is applied to the six meteorological stations of the Northern area, Pakistan. Moreover, the spatiotemporal weights obtained from STTSSWS are used to calculate MSTTSSWI for regional drought characterization. The MSTTSSWI may accurately provide regional spatiotemporal characteristics for the drought in the selected region and motivates researchers and policymakers to use the more comprehensive and accurate spatiotemporal characterization of drought in the selected region.

Discrete-Time Markov Chain Application to Population Growth Control in Lagos Metropolis, Nigeria

The study considered the birth gap with four states, length of breastfeeding with four states and type of contraceptives used with five states, by mothers with at least three conceptions in Lagos Metropolis, Nigeria. Data was obtained from the population using a self-designed and administered questionnaire. Results showed that the steady state probability of birth gap was highest at state 4 which is > 24 months implying that 3 out of five women on the long – run will space their births at more than 2 years which ultimately will lead to lower child birth, improved mother’s welfare and healthier children. Also, the distribution of mothers and their switching after each period of childbirth shows that contraceptives are indeed effective in controlling conception. Lastly, the transition probabilities of the states are significantly greater than zero and the state are dependent on each other (p < 0.05). The study therefore concluded that increased birth gaps, elongated length of breastfeeding and the use of contraceptives by mothers in Lagos Metropolis when combined will ultimately lead to slowing childbearing and population growth rate thereby serving as strong instruments in population growth control.

Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation

The present article presents the performance analysis of a non-Markovian machining system comprised of operating and standby machines together and functioning under N-policy for vacation. The prime motive of this investigation is to schedule the repairman’s vacation policy to return to the repair job as soon as the workload reaches a pre-defined threshold. The supplementary variable approach (SVT) is employed to establish the system steady-state probabilities, which are used to predict the other performance indices. The numerical illustrations have been provided to verify the outcomes of the proposed analytical model. For the design of optimal parameters at the minimum cost, numerical results are also provided using metaheuristic particle swarm optimization and genetic algorithm techniques

Risk assessment of medical devices used for COVID-19 patients based on a Markovian-based Weighted Failure Mode Effects Analysis (WFMEA)

Medical devices are critical in the healthcare system and their failures can significantly impress the safety of patients, medical staff, and clinical engineers. With the increasing COVID-19 pandemic in recent months, it is necessary to assess the risks of the devices to avoid infection for patients, death, and severe hurts due to inactive and breakdown devices. The aim of this study is to assess medical device risks in general and pandemic situations with three main factors of the Failure Model Analysis Effect include occurrence, detection, and severity. Some sub-factors are defined and weighted using the Fuzzy DEMATEL and Fuzzy Best-Worst Method. Consequently, the weighted FMEA score of each failure is calculated as the Weighted Risk Priority Number. Finally, steady-state probabilities of very low and low failures are calculated to consider the changes during the time. Results show that near half of the failures are scored in very low and low levels but in the long term, most of them transfer to medium level risk. It can be concluded that some preventive maintenance plans for these kinds of failures to avoid occurring the higher risk level for them in the future is necessary and the results can help medical device managers.

A multi-station unreliable machine model with working vacation policy and customers’ impatience

ABSTRACT Working vacation queues with breakdowns and customers impatience have many applications in different real-life situations. The development of these models to determine their performance is extremely important. In this paper, we deal with a finite population Markovian multi-server machine system with breakdowns, repairs, Bernoulli feedback, balking, reneging, and retention of reneged customers, under multiple synchronous working vacations. The investigated model has a potential application in the real-world machine systems, such as the automated manufacturing systems with limited space. For the analysis purpose, we employ Q-matrix method in order to obtain the steady-state probabilities as well as closed-form expressions for several system characteristics. Particular cases of the current study are presented. We construct the expected cost function and develop an optimization problem to determine the optimum cost. The direct search method and the Quasi–Newton method are applied to find the optimum system capacity, the minimum number of servers, and the optimum service rates during both working vacation and regular busy periods at minimum cost. Lastly, a sensitivity analysis for the numerical simulation is carried out.

Schubert Polynomials, the Inhomogeneous TASEP, and Evil-Avoiding Permutations

Abstract Consider a lattice of n sites arranged around a ring, with the $n$ sites occupied by particles of weights $\{1,2,\ldots ,n\}$; the possible arrangements of particles in sites thus correspond to the $n!$ permutations in $S_n$. The inhomogeneous totally asymmetric simple exclusion process (or TASEP) is a Markov chain on $S_n$, in which two adjacent particles of weights $i<j$ swap places at rate $x_i - y_{n+1-j}$ if the particle of weight $j$ is to the right of the particle of weight $i$. (Otherwise, nothing happens.) When $y_i=0$ for all $i$, the stationary distribution was conjecturally linked to Schubert polynomials [18], and explicit formulas for steady state probabilities were subsequently given in terms of multiline queues [4, 5]. In the case of general $y_i$, Cantini [7] showed that $n$ of the $n!$ states have probabilities proportional to double Schubert polynomials. In this paper, we introduce the class of evil-avoiding permutations, which are the permutations avoiding the patterns $2413, 4132, 4213,$ and $3214$. We show that there are $\frac {(2+\sqrt {2})^{n-1}+(2-\sqrt {2})^{n-1}}{2}$ evil-avoiding permutations in $S_n$, and for each evil-avoiding permutation $w$, we give an explicit formula for the steady state probability $\psi _w$ as a product of double Schubert polynomials. (Conjecturally, all other probabilities are proportional to a positive sum of at least two Schubert polynomials.) When $y_i=0$ for all $i$, we give multiline queue formulas for the $\textbf {z}$-deformed steady state probabilities and use this to prove the monomial factor conjecture from [18]. Finally, we show that the Schubert polynomials arising in our formulas are flagged Schur functions, and we give a bijection in this case between multiline queues and semistandard Young tableaux.

Computation of Steady-State Probabilities of the states of the SMP model in Beacon Message Dissemination

Wydawnictwo SIGMA-NOT wydaje czasopisma fachowe informujące swoich czytelników o najnowszych osiągnięciach naukowych i nowoczesnych rozwiązaniach technicznych w Polsce i na świecie, popularyzuje problemy techniczne oraz poszerza wiedzę i kulturę techniczną.

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.

Performance evaluation for secondary users in finite-source cognitive radio networks with dynamic preemption limit

Primary users (PUs) have higher priority and are able to preempt the channels used by secondary users (SUs) in cognitive radio networks (CRNs). The traditional complete preemption mechanism does not restrict the preemption behavior of PUs, and it isn’t easy to guarantee SUs’ transmission performance when PU packets arrive frequently. To ensure SUs’ most essential continuous transmission, we propose a preemption mechanism with a dynamic preemption limit in a finite-source CRN system. The preemption limit is adjusted dynamically by the central controller in accordance with transmitted SU packets’ quantity to restrict PUs’ preemption behavior. We develop a 2-dimensional Markov-chain based on this to construct a discrete-time preemptive queueing model. With the solved system’s steady-state probability distribution, we obtain some performance index expressions. Moreover, we analyze the system’s performance in various network conditions and compare our proposed preemption mechanism to the traditional complete preemption mechanism to demonstrate its superiority by employing numerical experiments. Numerical results show that the proposed preemption mechanism with a dynamic preemption limit can improve SUs’ transmission performance and adapt to the more complex network environments. Finally, we create a utility function to calculate the ideal amount of SUs that will provide the optimal comprehensive performance.

A comparative analysis of pre- and post-industrial spatiotemporal drought trends and patterns of Tibet Plateau using Sen slope estimator and steady-state probabilities of Markov Chain

A comparative analysis of pre- and post-industrial spatiotemporal drought trends and patterns of Tibet Plateau using Sen slope estimator and steady-state probabilities of Markov Chain

Time Delay in Engagement Schedules in a Public University in Ghana

This paper aims to examine the incidence of time delays in engagement schedules on campus. The study made use of past records of time delays in starting committee meetings of five colleges at a public university in Ghana. The study relied on secondary data extracted from minute and agenda files of college meetings. The Minitab package and Microsoft Spreadsheet were used to analyse the data. The statistical techniques used in the study were Markov prosses and Steady state probability. The results revealed that the College of Agriculture and Natural Sciences consistently start their meetings on-time in the long-run with the highest probability of approximately 0.810. Meetings of the College of Education is characterized with large delays in starting times in the long-run with the highest probability of approximately 0.812. Based on the results, the paper recommends that the colleges with higher possibility of starting their meetings ten minutes late should encourage its board or committee members to be prompt in attending to meeting/schedules. Additionally, the paper suggests that the management of the university should design an effective policy to ensure a rescheduling when a meeting delays for more than an hour.

A stochastic mobility model for traffic forecasting in urban environments

With the steadily growing traffic demand, urban traffic congestion is becoming a critical issue threatening several factors, including public safety, emissions of greenhouse gas, and transport inefficiencies. Thus, intelligent transport systems (ITS) have emerged as a promising solution to easing the burden of congestion. ITS rely on different technologies such as VANET (Vehicular Adhoc Networks) which provide the transportation system with ubiquitous connectivity allowing the exchange of traffic information between vehicles and roadside terminals. This can support numerous smart mobility applications such as traffic signal control and real-time traffic management. Hence, mobility models were developed to emulate and forecast the distribution of traffic which will be helpful to the design and management of traffic control strategies. In this context, this study specifically concentrates on developing a mobility model that reflects vehicular activities in urban environments based on vehicular information collected using vehicular communications. The behavior of vehicles along multi-lane roads and intersections is modeled as a stochastic process using queuing theory. Particularly, the queue system is analyzed as a continuous-time Markov chain (CTMC) and by calculating the steady-state probabilities, different performance measures are derived and analyzed under various scenarios. To validate the model, the obtained forecasts are compared with a queue model and realistic traces. The results show that the model is capable of reproducing the realistic behavior of traffic in urban roads without incurring heavy costs and time-consuming computing. The obtained estimates were then used to design an actuated traffic light and a vehicle speed adaptor. From the simulation results, it is clear that using the proposed traffic forecasting model helps reduce vehicles idling and travel times.

Tipping the Balance: A Criticality Perspective.

Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP). Under steady state conditions, the model has similarities with a well-known model of population genetics which exhibits a purely noise-induced transition from unimodality to bimodality at a critical value of the noise intensity . The noise is associated with the parameter λ representing the system-environment coupling. In the case of the tumour model, λ has a natural interpretation in terms of the tissue microenvironment which has considerable influence on the phenotypic composition of the tumour. Oncogenic transformations give rise to considerable fluctuations in the parameter. We compute the phase diagram in a stochastic setting, drawing analogies between bifurcations and phase transitions. In the region of bimodality, a transition from a state of balance to a state of dominance, in terms of the competing subpopulations, occurs at λ = 0. Away from this point, the NCP (CP) subpopulation becomes dominant as λ changes towards positive (negative) values. The variance of the steady state probability density function as well as two entropic measures provide characteristic signatures at the transition point.