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We considered two periodic review perishable inventory systems. The first system is controlled by a periodic review (T , S) policy, where orders are triggered at each review period T and when the stock is less than S. The second one is controlled by a periodic review (s , S) policy, where orders are triggered only if the stock level is below s. For both models, the lifetime of each product was assumed to follow a general distribution, whereas the lead time was constant. The demands followed a Poisson process, and all unsatisfied demand was lost. Using an approximate solution of the steady-state probabilities of the inventory level, we obtained a closed form of cost expression. Next, we conducted a simulation study to identify our solution accuracy. Finally, we performed a sensitivity analysis to evaluate the effect of the lifetime variation and cost parameters on the best policy and its cost. The obtained results were close to those of the optimal policy with an average accuracy of 3.7% for the periodic review (T , S) policy and 3.8% for the periodic review (s , S) policy. For the worst cases, where the accuracy is higher than 7%, we provided an analytical approach to improve the system accuracy. [ABSTRACT FROM AUTHOR]

We consider the general diffusion equation driven by tempered fractional Brownian motion (TFBM) ∂ u (t , x) ∂ t = L u (t , x) + u (t , x) d B H , λ (t) d t , (t , x) ∈ R + × R d , where L is the infinitesimal generator of some time-homogeneous Markov process { X t } t ≥ 0 and { B H , λ (t) } t ∈ R is a tempered fractional Brownian motion with Hurst index H ∈ (0 , 1 2) ∪ (1 2 , 1) and tempering parameter λ > 0 which is independent of { X t } t ≥ 0. Based on approximating TFBM with a family of Gaussian processes possessing absolutely continuous sample paths, a unified framework of the Feynman-Kac formula u (t , x) = E x [ f (X t) ] e B H , λ (t) is established for the general stochastic diffusion equation driven by TFBM with the initial value f , Hurst index H ∈ (0 , 1 2) ∪ (1 2 , 1) and tempering parameter λ > 0. The difficulty is that the Hurst parameter H can be allowed to be less than 1/2. The idea is to explore the above simplest form, to utilize the techniques of Malliavin calculus. By using the properties of TFBM and especially that of the modified Bessel function of the second kind, we prove that the process defined by the Feynman-Kac formula is the mild and weak solutions of the general diffusion equation driven by TFBM. From the Feynman-Kac formula, we exhibit the smoothness of the density of the solution and the sharp Hölder regularity. We further show that lim t → ∞ ⁡ ln ⁡ ‖ u (t , ⋅) ‖ p g (t) = 0 in the almost surely sense where p ∈ R and the function g : R + → R + grows at least as fast as a linear function. The Feynman-Kac formula for the stochastic general diffusion equation in the Skorohod sense is also achieved by exploring the relationship between the Stratonovich and Skorohod integrals. [ABSTRACT FROM AUTHOR]

• A novel degradation process with abrupt jumps caused by operation state transition is proposed. • Analytical reliability solutions of the model are derived in the form of one-dimensional Laplace-Stieltjes transform. • The limit reliability solutions are investigated, as alternative strategy under long-term service. • Analytical solutions regarding statistical characteristics of degradation amount during regeneration epoch are proposed. • The case of spool valve is implemented to verify the effectiveness and the feasibility of the solutions. This paper proposes a novel type of degradation process incorporating continuous degradation and abrupt degradation jump under dynamic operation states. By analyzing the failure mechanism of practical application, the abrupt degradation jump is comprehensively considered, and it is triggered by some certain state switching processes. Then, the reliability solutions of the degradation process (reliability function and moments of lifetime) are derived in the form of Laplace-Stieltjes transform. To a further step, inspired by the advanced equipment with long service span, the reliability solutions in limit region are explored, where an effective calculation method regarding statistical characteristics of degradation amount during regeneration epoch is pioneeringly proposed. To verify the proposed solutions in the form of Laplace-Stieltjes transform and their limit case, the representative example, spool valve, is implemented, and the results show the effectiveness and the feasibility of the solutions. [ABSTRACT FROM AUTHOR]

With the development of economic globalization and increasing international trade, the maritime transportation system (MTS) is becoming more and more complex. A failure of any supply line in the MTS can seriously affect the operation of the system. Resilience describes the ability of a system to withstand or recover from a disaster and is therefore an important method of disaster management in MTS. This paper analyzes the impact of disasters on MTS, using the data of Suez Canal "Century of Congestion" as an example. In practice, the severity of a disaster is dynamic. This paper categorizes disasters into different levels, which are then modelled by the Markov chain. The concept of a repair line set is proposed and is determined with the aim to minimize the total loss and maximize the resilience increment of the line to the system. The resilience measure of MTS is defined to determine the repair line sequence in the repair line set. Finally, a maritime transportation system network from the Far East to the Mediterranean Sea is used to validate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to examine the behavior of certain industrial systems under the conditions of product warranty policy. Given this policy, we are interested in considering all the parameters of the system in order to study them and show their impact on the proposed system. In order to increase the efficiency of the system and activate the product warranty policy, the system will undergo a preliminary examination for any system failure occurrence to determine the reasons that led to the failure. After completing the initial inspection, the mechanic will decide whether it is a user-caused failure or a manufacturing defect to determine whether or not the repair of the broken appliance is covered by the manufacturer's contractual warranty policy. All times in the system are assumed as a negative exponential distribution. The expressions for some measures of system effectiveness such as reliability, mean time to system failure (MTSF), and availability are derived using the supplementary variable technique and Laplace transform. Sensitivity analysis and a relative sensitivity are then carried out in order to recognize how each system parameter affects performance measures. Finally, some numerical examples are designed and performed to show how the change of each system parameter affects system performance. [ABSTRACT FROM AUTHOR]

This article presents an exploration of mathematical modeling and performance enhancement of a casting system in the steel industry. The study employs the implementation of Markov processes and genetic algorithm to achieve these objectives. The system comprises of four subsystems namely transfer laddle, continuous casting machine, shot blasting machine and grinding machine. These are arranged in a way that failing of a single subsystem halts the working of overall system. Using probabilistic approach, differential equations have been developed from transition diagram based on Markov process. Failure and repair rates follow exponential distribution. To ascertain steady state availability, differential equations are solved using normalizing conditions. Further, genetic algorithm is applied to find optimal values of failure/repair rates to estimate the optimal plant availability. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic analysis of the hitting time of Markov-type jump processes (i.e., semi-Markov, Markov, in continuous or discrete time) with a small probability of entering a non-empty terminal subset. This means that absorption is a rare event. The mean hitting time function of all four type processes obeyed the same equation. We obtain unified results of asymptotic approximation in a series scheme or, equivalently, a functional type of mean hitting time. [ABSTRACT FROM AUTHOR]

In this paper, we present a general formula to calculate transition probabilities for six different types of systems based on their redundancy strategy and the status of the components. The systems are under periodic inspection policy and their components are repairable. The investigated systems include system I – active redundancy without any component to be replaced or repaired; system II – active with the component(s) to be replaced and repaired; system III – active with the component(s) to be repaired; system IV – standby without any component(s) to be replaced or repaired; system V – standby with the component(s) to be replaced and repaired; and system VI – standby with the component(s) to be repaired. In addition, all components in a system are considered non-identical. To calculate the transition probabilities for systems IV, V, and VI, we first consider a system with n non-identical components and cold standby configuration (NIC-CSC) and calculate the system state probabilities using Markov theory. Then, we present the general formula transition probabilities for systems IV, V, and VI using the results of the NIC-CSC system inspection interval. We demonstrate how to calculate the transition probabilities and matrixes for the six above-mentioned systems using the provided formulas. Moreover, we use the provided formulas to optimize the inspection interval of these systems using a modified full enumeration technique. [ABSTRACT FROM AUTHOR]

We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it. [ABSTRACT FROM AUTHOR]

A crisp step function is not an adequate threshold for studies of Markovian occurrence of large earthquakes, because it can lead to missing or pseudo links in an observed sequence that should be a Markov chain. A more realistic threshold is a fuzzy one where there is a transition magnitude band, located between those magnitudes that are too small for the earthquakes to be part of a Markovian process and those who are certainly large enough for the earthquakes to be part of it, where earthquakes may or may not be part of the process. This fuzzy threshold is described by a membership function that gives the probability of an earthquake with a given magnitude belonging to the process. We propose a membership function with probabilities in the transition band proportional to the seismic moment. To estimate empirical transition probabilities when considering a fuzzy magnitude threshold, we propose a counting strategy for the observed transitions and justify it through Monte Carlo simulations. The counting strategy is illustrated by application to the model from a previous seismic study of the Japan area by testing, through Monte Carlo simulations, how well the counting strategy results resemble optimum estimations of the transition probabilities. The simulations are also used to study the behavior of three Markovianity measures, and it is found that the peak values of these measures are not useful in identifying the true transition band, but that this band may be better identified by using the whole set of values taken by each measure for different transition band models. As an illustration, the measures were applied to real data from the previous study, a short set corresponding to a single realization, and found that the behavior of the measures does not agree with those expected from a crisp threshold, but agree, within the limitations of the data, with either a fuzzy threshold going from zero probability for magnitudes M ≤ 6.9 to probability one for M ≥ 7.2 or from zero probability for magnitudes M ≤ 7.0 to probability one for M ≥ 7.2 . [ABSTRACT FROM AUTHOR]

We study the evolution of the friendship index in complex social networks over time. The elements of the networks are the users, and the connections correspond to the interactions between them. The friendship index of a node is defined as the ratio of the average degree of its neighbors to the degree of the node itself. Obviously, in the process of network growth, the value of the friendship index for any node in the network may change due to the fact that new edges can be attached to this node or its neighbors. In this paper, we study the dynamics of the friendship index of a single node over time for growth networks generated on the basis of the preferential attachment mechanism. We find both the asymptotics of their expected values and the variances over time. In addition, we analyze the behavior of the friendship index for five real networks.

This article studies the output feedback control (OFC) issue for fuzzy Markov jump systems with actuator faults and deception attacks. To describe the nonlinear characteristics, the Takagi–Sugeno (T–S) fuzzy rule scheme is utilized. A general network environment with deception attacks is considered, and Bernoulli distributed variable is adopted to describe the randomly occurring attacks. To alleviate the actuator faults and attacks in the networked data transmission, a new reliable OFC protocol is forwarded to ensure the prescribed system performance. Meanwhile, a hidden Markov model is resorted to treat the nonsynchronous phenomena between system mode and controller mode. By a stochastic Lyapunov function, some criteria are proposed such that the closed-loop dynamic is stochastically stable. Finally, the effectiveness and application of the obtained results are confirmed by a physical mass-spring-damper model. [ABSTRACT FROM AUTHOR]

Abstract Background Extended illness-death models (a specific class of multistate models) are a useful tool to analyse situations like hospital-acquired infections, ventilation-associated pneumonia, and transfers between hospitals. The main components of these models are hazard rates and transition probabilities. Calculation of different measures and their interpretation can be challenging due to their complexity. Methods By assuming time-constant hazards, the complexity of these models becomes manageable and closed mathematical forms for transition probabilities can be derived. Using these forms, we created a tool in R to visualize transition probabilities via stacked probability plots. Results In this article, we present this tool and give some insights into its theoretical background. Using published examples, we give guidelines on how this tool can be used. Our goal is to provide an instrument that helps obtain a deeper understanding of a complex multistate setting. Conclusion While multistate models (in particular extended illness-death models), can be highly complex, this tool can be used in studies to both understand assumptions, which have been made during planning and as a first step in analysing complex data structures. An online version of this tool can be found at https://eidm.imbi.uni-freiburg.de/ .

The article proposes a concept of organizing access to the guaranteed resource of the 5 G cluster information environment, structured in the form of a hierarchy of logical network segments. This framework presents an interrupt access control scheme that exhibits survivability characteristics important to mission-critical applications. Analytically, the author's concept is represented by an irreversible Markov process, for which a system of equilibrium equations and stationary probabilities are defined. Based on the latter, a qualitative metric was formulated, which included such indicators as the average number of requests accepted for service in the 5 G cluster, the probability of losing an incoming request, and the average volume of network resource units used in the 5 G cluster. For the single input data that characterizes a real NS 5 G cluster, a comparison of the author's and known competing access control schemes in terms of formulated qualitative metrics is implemented. The obtained results showed that the author's concept prevails over the competitor in the range of low loads. Note that in this range, the advantage of the author's scheme over the competitor significantly increases with the increase in the number of network segments into which the information environment of the 5 G cluster is divided.

AbstractA multi-state m-out-of-r-within-k-out-of-n system has found great importance in reliability theory because of its wide applications in engineering systems. In previous studies, usually all the components of the m-out-of-r-within-k-out-of-n system were considered to be binary and that too in a steady state, despite the fact that there are numerous complex systems where the components of this type of system can be multi-state and dynamic in nature i.e., their states change over time. To deal with this circumstance, the current research presents an algorithm, based on the Lz-transform to determine the reliability indices of the considered system in the dynamic setup. The Markov process is assumed to be followed by the components of the considered system and is mended only after they entirely fail. In the proposed research, reliability, availability, instantaneous mean expected performance and mean performance deficiency are obtained for the considered system. Finally, a case study of the photovoltaic system is studied to implement and validate the proposed method. [ABSTRACT FROM AUTHOR]

Reverse mortgage is one of the products (perhaps the main one) that is good to obtain additional income by using the habitual residence as collateral. The main objective of this paper is to analyse the effects that reverse mortgage contracting has on household finances over the lifetime of a family according to the socioeconomic group to which it belongs in Spain. Four indicators are employed to measure the immediate and long-term effects. We use a stochastic model with a double source of randomness, survival and entry into dependency, and apply it to the three socioeconomic groups obtained with cluster methodology from the 2017 Spanish Household Financial Survey data. We conclude that the effects are very different depending on the group: regarding only the effects of hiring a reverse mortgage on the income of the family, widowed women aged between 81 and 85 years, with low income and expenses as well as little net wealth, and a habitual residence that represents half of her net wealth (Cluster 1) are the most benefited; considering that the highest impact indicators are on the probability of illiquidity and on the value of lack of liquidity, the use of reverse mortgages benefits more the families in Cluster 3 (high income and expenses and really high net wealth, head of household aged between 76 and 80 years) and less the families in Cluster 2 (medium income, net wealth and expenses, head of household aged between 65 and 75 years). [ABSTRACT FROM AUTHOR]

Accepted by: Phil Scarf We model tactical changes in association football as a Markov game. The pitch is discretized into nine zones and the states of the Markov game are defined according to the zone in which the ball is located in-play, the team in possession and the score. We first model tactical changes in a Markov decision process framework, wherein one team maximizes their probability of winning. Then, we model tactical changes in a two-person zero-sum Markov game framework, wherein both teams maximize their probability of winning. Fundamental to our modelling is the notion that tactical changes impact upon transition rates. We verify the models using data from matches in a season of the Japan Professional Football League. We define a change in transition rates that can be realized by changes in tactics, and illustrate an example of optimal tactical changes when both teams can vary their tactics. The models we develop in the paper can support managers who are considering important decisions about substitutions and changes to formation, for example, when a match is in-play. [ABSTRACT FROM AUTHOR]

This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation value of an optimal stopping problem can be approximated with error at most ε by a deep ReLU neural network of size at most κ d q ε − r . The constants κ , q , r ≥ 0 do not depend on the dimension d of the state space or the approximation accuracy ε . This proves that deep neural networks do not suffer from the curse of dimensionality when employed to approximate solutions of optimal stopping problems. The framework covers for example exponential Lévy models, discrete diffusion processes and their running minima and maxima. These results mathematically justify the use of deep neural networks for numerically solving optimal stopping problems and pricing American options in high dimensions. [ABSTRACT FROM AUTHOR]

The latent state–trait theory posits that a psychological construct may reflect stable influences specific to a person (i.e., trait), ephemeral influences from situations (i.e., state), and interactions between them (i.e., state–trait interactions). Researchers conventionally apply mixture modelling to explore heterogeneity in variables by identifying homogenous classes with respect to the measured variable, yet rarely distinguishing between person‐ and situation‐specific classes. The current study introduces novel categorical latent state–trait models to identify subgroups in states and traits, quantifying the effects of person‐specific classes, situation‐specific classes, and person–situation interactions. The proposed models are applied to an empirical dataset. We discuss statistical inference, effect size measures, and model visualization for the proposed models. Based on realistic parameter values from the empirical dataset, preliminary simulation studies were conducted to investigate models’ performances. Bayesian estimation in the proposed models allows flexible testing of a wide range of hypotheses related to state, trait, and interaction effects. We discuss limitations and future directions. [ABSTRACT FROM AUTHOR]

The multi-task allocation has become the key to be solved urgently in applying a coal gangue sorting robot system (CGSRS) in raw coal with high throughput. This paper constructs a multi-task allocation framework of CGSRS for time-varying raw coal flow (TVRCF), including task decomposition, task allocation, and collaborative strategy. Establish the TVRCF decomposition model using the tumbling time window method to obtain the gangue model. A multi-task allocation model based on M/M/s queuing model with impatient customers is proposed because arrival time, granularity, and spatial position of the gangue model are uncertain. By introducing trajectory function and designing benefit function, to solve environment states of sorting area. Creating an iterative mechanism for environment states based on the infinite Markov process, using service time and arrival time interval. An adaptive weights rule based on the greedy algorithm (GAW) is proposed to improve the benefit of multi-task allocation. Simulating 18 groups of TVRCF with 9 productivity. Experimental results show that the proposed framework suits the multi-task allocation of CGSRS to TVRCF. The GAW rule always ensures the optimal sorting rate, the near-optimal task completion success rate, and the manipulator utilization rate. In addition, the stability of the GAW rule is best. [ABSTRACT FROM AUTHOR]

We study Markov population processes on large graphs, with the local state transition rates of a single vertex being a linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the homogeneous mean-field approximation (HMFA). Our main result is showing that HMFA is guaranteed to be the large graph limit of the stochastic dynamics on a finite time horizon if and only if the graph-sequence is quasi-random. An explicit error bound is given and it is 1 N plus the largest discrepancy of the graph. For Erdős–Rényi and random regular graphs we show an error bound of order the inverse square root of the average degree. In general, diverging average degrees is shown to be a necessary condition for the HMFA to be accurate. Under special conditions, some of these results also apply to more detailed type of approximations like the inhomogenous mean field approximation (IHMFA). We pay special attention to epidemic applications such as the SIS process. [ABSTRACT FROM AUTHOR]

Background: Extended illness-death models (a specific class of multistate models) are a useful tool to analyse situations like hospital-acquired infections, ventilation-associated pneumonia, and transfers between hospitals. The main components of these models are hazard rates and transition probabilities. Calculation of different measures and their interpretation can be challenging due to their complexity. Methods: By assuming time-constant hazards, the complexity of these models becomes manageable and closed mathematical forms for transition probabilities can be derived. Using these forms, we created a tool in R to visualize transition probabilities via stacked probability plots. Results: In this article, we present this tool and give some insights into its theoretical background. Using published examples, we give guidelines on how this tool can be used. Our goal is to provide an instrument that helps obtain a deeper understanding of a complex multistate setting. Conclusion: While multistate models (in particular extended illness-death models), can be highly complex, this tool can be used in studies to both understand assumptions, which have been made during planning and as a first step in analysing complex data structures. An online version of this tool can be found at https://eidm.imbi.uni-freiburg.de/. [ABSTRACT FROM AUTHOR]

We consider finite graphical n-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in stationary mixed strategies, we introduce probability distributions in all non-terminal positions. The corresponding probability distributions on the set of plays can be defined in two different ways called the Markov and a-priori realizations. The former one guarantees existence of a uniform best response for each player in every situation. Nevertheless, Nash equilibrium may fail to exist even in stationary mixed strategies. The classical Nash's theorem is not applicable, because in this case limit distributions and expected payoffs may be discontinuous. Although a-priori realizations do not share many nice properties of the Markov ones (for example, the existence of uniform best responses) but in return, Nash's theorem is applicable. We illustrate both realizations in details by two examples with 2 and 3 players. We also survey some general results related to Nash-solvability, in pure and mixed stationary strategies, of stochastic n-person games with perfect information and n-person graphical games among them. [ABSTRACT FROM AUTHOR]

This paper explores memory mechanisms in complex socio-technical systems, using a mobility demand model as an example case. We simplify a large-scale agent-based mobility model, formulate the corresponding stochastic process, and observe that the mobility decision process is non-Markovian. This is due to its dependence on the system's history, including social structure and local infrastructure, which evolve based on prior mobility decisions. Complementing the mobility process with two history-determined components leads to an extended mobility process that is Markovian. Although our model is a very much reduced version of the original one, it remains too complex for the application of usual analytic methods. Instead, we employ simulations to examine the functionalities of the two history-determined components. We think that the structure of the analyzed stochastic process is exemplary for many socio-technical, -economic, -ecological systems. Additionally, it exhibits analogies with the framework of extended evolution, which has previously been used to study cultural evolution. [ABSTRACT FROM AUTHOR]

The article proposes a concept of organizing access to the guaranteed resource of the 5 G cluster information environment, structured in the form of a hierarchy of logical network segments. This framework presents an interrupt access control scheme that exhibits survivability characteristics important to mission-critical applications. Analytically, the author's concept is represented by an irreversible Markov process, for which a system of equilibrium equations and stationary probabilities are defined. Based on the latter, a qualitative metric was formulated, which included such indicators as the average number of requests accepted for service in the 5 G cluster, the probability of losing an incoming request, and the average volume of network resource units used in the 5 G cluster. For the single input data that characterizes a real NS 5 G cluster, a comparison of the author's and known competing access control schemes in terms of formulated qualitative metrics is implemented. The obtained results showed that the author's concept prevails over the competitor in the range of low loads. Note that in this range, the advantage of the author's scheme over the competitor significantly increases with the increase in the number of network segments into which the information environment of the 5 G cluster is divided. [ABSTRACT FROM AUTHOR]

The first step in the road handling effort is to survey to get an accurate road condition value to take correct action in implementing maintenance. As pavement performance is known to be probabilistic, various levels of uncertainty must be assumed. Modern pavement management methods are ineffective without an effective model to predict pavement performance. Discrete-time Markov chains are the most widely used probabilistic models, and examples from different countries worldwide can be found in pavement management systems. This research aims to predict the value of road conditions during maintenance and compare road assessments with real conditions during road maintenance using the IRI, SDI, and PCI methods using the Markov process. The analysis method used is to collect secondary data from related departments and carry out direct data collection in the field to obtain condition values based on IRI, SDI, and PCI to forecast by making a pavement condition prediction model based on the Markov process and then assessing road conditions by comparing the three index values with the slightest deviation value. The analysis showed that the average value of road conditions with the IRI indicator is 4.45, which is moderate, and the most negligible difference between the probability distribution of pavement condition prediction modeling and the actual survey results was the IRI (International Roughness Index) method. This model is closest to the actual conditions during implementation, with a difference value of 5.7%. [ABSTRACT FROM AUTHOR]

Thermal energy storage (TES) offers a practical solution for reducing industrial operation costs by load-shifting heat demands within industrial processes. In the integrated Thermomechanical pulping process, TES systems within the Energy Hub can provide heat for the paper machine, aiming to minimize electricity costs during peak hours. This strategic use of TES technology ensures more cost-effective and efficient energy consumption management, leading to overall operational savings. This research presents a novel method for optimizing the design and operation of an Energy Hub with TES in the forest industry. The proposed approach for the optimal design involves a comprehensive analysis of the dynamic efficiency, reliability, and availability of system components. The Energy Hub comprises energy conversion technologies such as an electric boiler and a steam generator heat pump. The study examines how the reliability of the industrial Energy Hub system affects operational costs and analyzes the impact of the maximum capacities of its components on system reliability. The method identifies the optimal design point for maximizing system reliability benefits. To optimize the TES system's charging/discharging schedule, an advanced predictive method using time series prediction models, including LSTM (Long Short-Term Memory) and GRU (Gated Recurrent Unit), has been developed to forecast average daily electricity prices. The results highlight significant benefits from the optimal operation of TES integrated with Energy Hubs, demonstrating a 4.5–6 percent reduction in system operation costs depending on the reference year. Optimizing the Energy Hub design improves system availability, reducing operation costs due to unsupplied demand penalty costs. The system's peak availability can reach 98 %, with a maximum heat pump capacity of 2 MW and an electric boiler capacity of 3.4 MW. The GRU method showed superior accuracy in predicting electricity prices compared to LSTM, indicating its potential as a reliable electricity price predictor within the system.

The emergence and dynamic prevalence of genetic disorders and infectious diseases with mutations pose significant challenges for public health interventions. This study investigated the parameter estimation approach and the application of the dynamic state-space Markov modeling of these conditions. Using extensive simulations, the model demonstrated robust parameter estimation performance, with biases and mean-squared errors decreasing as sample size increased. Applying the model to COVID-19 data revealed distinct temporal patterns for each variant, highlighting their unique emergence, peak dominance, and decline or persistence trajectories. Despite the absence of clear trends in the data, the model exhibited a remarkable accuracy in predicting future prevalence trends for most variants, showcasing its potential for real-time monitoring and analysis. While some discrepancies were observed for specific variants, these findings suggest the model’s promise as a valuable tool for informing public health strategies. Further validation with larger datasets and exploration of incorporating additional factors hold the potential for enhancing the model’s generalizability and applicability to other evolving diseases.

Redundancy is a well-known concept for system resilience; k-out-of-n redundancy stipulates that a minimum number of functional components must be present for the system to function. Introducing a reboot delay acknowledges the temporal complexities of system recovery after a failure. A dynamic component is added by the vacation policy, which introduces strategic downtime for system components. This work predicts the performance measures of a multi-state system consisting of two subsystems A and B. Subsystem A follows the k-out-of-n: F policy and subsystem B has m working units and s warm standby units. The system is under the consideration of a single unreliable repairman who may go allow for vacation. There are two possibilities for a repairman’s vacation: if the system failed and the repairman is on vacation, in that case, if the repairman immediately returns from vacation, he/ she repairs the system but if the repairman does not return immediately from vacation, then the system takes a reboot action and when the repairman available, he/ she repairs the system. Failure and repair time of the units are expected to pursue an exponential distribution. In addition, the vacation time and reboot time regarding the failure of the units also pursue an exponential distribution. The concept of reboot and repairman’s vacation are incorporated to make the model more practical and versatile. The expressions for several performance measures such as availability, reliability, and MTTF are obtained with the help of the Markov process. Likewise, sensitivity analysis is done to study the impact of various parameters on system performance measures. The results are explained by taking numerical illustrations.

In this study, we developed a dynamical Multi-Local-Worlds (MLW) complex adaptive system with co-evolution of agent's behavior and local topological configuration to predict whether agents' behavior would converge to a certain invariable distribution and derive the conditions that should be satisfied by the invariable distribution of the optimal strategies in a dynamical system structure. To this end, a Markov process controlled by agent's behavior and local graphic topology configuration was constructed to describe the dynamic case's interaction property. After analysis, the invariable distribution of the system was obtained using the stochastic process method. Then, three kinds of agent's behavior (smart, normal, and irrational) coupled with corresponding behaviors, were introduced as an example to prove that their strategies converge to a certain invariable distribution. The results showed that an agent selected his/her behavior according to the evolution of random complex networks driven by preferential attachment and a volatility mechanism with its payment, which made the complex adaptive system evolve. We conclude that the corresponding invariable distribution was determined by agent's behavior, the system's topology configuration, the agent's behavior noise, and the system population. The invariable distribution with agent's behavior noise tending to zero differed from that with the population tending to infinity. The universal conclusion, corresponding to the properties of both dynamical MLW complex adaptive system and cooperative/non-cooperative game that are much closer to the common property of actual economic and management events that have not been analyzed before, is instrumental in substantiating managers' decision-making in the development of traffic systems, urban models, industrial clusters, technology innovation centers, and other applications.

Laboratory experiments are one of the important means used to investigate travel choice behavior under strategic uncertainty. Many experiment-based studies have shown that the Nash equilibrium can predict aggregated route choices, while the fluctuations, whose mechanisms are still unclear, continue to exist until the end. To understand the fluctuations, this paper proposes a route-dependent attraction-based stochastic process model, which shares exactly the same behavioral foundation introduced in Part I of the study (Qi et al., 2023), i.e., route-dependent inertia and route-dependent preference. The model predictions are carefully compared with the experimental observations obtained from the congestible parallel-route laboratory experiments containing 312 subjects and eight decision-making scenarios (Qi et al., 2023). The results show that the proposed stochastic process model can precisely reproduce the random oscillations both in terms of flow switching and route flow evolution. Subsequently, an approximated model is developed to enhance the efficiency in evaluating the equilibrium distribution, providing a practical tool to evaluate the impacts of transportation policies in both long- and short-term runs. To the best of our knowledge, this paper is the first attempt to model and explain experimental phenomena by introducing stochastic process theories, as well as a successful example of applying experimental economics methodology to improve our understanding of human travel choice behavior.

This study looks into the numerous reliability aspects of a series–parallel system. The designed system is made up of the three subsystems A, B, and C that interconnected in a series–parallel manner. Subsystem B has two units, whereas subsystems A and C have a single unit. Here, the system reliability measures such as reliability, availability, and mean time to failure using Laplace transformation and Markov's process are evaluated. This study deals with minimize cost while system having the maximum reliability as constraining from one of the metaheuristic algorithms i.e., Particle Swarm Optimization (PSO). Lastly, a numerical example and graphical representation has been shown that the proposed methods are effective and efficient for solving reliability measures and cost problems. [ABSTRACT FROM AUTHOR]

Accepted by: M. Zied Babai In the medical service system, when the number of expert seats is in short supply, it is difficult to make full use of hospital resources by the traditional queuing method. Without changing the existing resources, an overflow model with triage in a Markov queuing system is established by overflowing a part of patients in the expert queue into the general queue under a certain condition to allocate reasonably the capacity of each outpatient. The numerical simulation using ProModel, a simulation software, shows that the average queue length, waiting time and other service indices are better than the traditional models. [ABSTRACT FROM AUTHOR]

Redundancy is a well-known concept for system resilience; k-out-of-n redundancy stipulates that a minimum number of functional components must be present for the system to function. Introducing a reboot delay acknowledges the temporal complexities of system recovery after a failure. A dynamic component is added by the vacation policy, which introduces strategic downtime for system components. This work predicts the performance measures of a multi-state system consisting of two subsystems A and B. Subsystem A follows the k-out-of-n: F policy and subsystem B has m working units and s warm standby units. The system is under the consideration of a single unreliable repairman who may go allow for vacation. There are two possibilities for a repairman's vacation: if the system failed and the repairman is on vacation, in that case, if the repairman immediately returns from vacation, he/she repairs the system but if the repairman does not return immediately from vacation, then the system takes a reboot action and when the repairman available, he/she repairs the system. Failure and repair time of the units are expected to pursue an exponential distribution. In addition, the vacation time and reboot time regarding the failure of the units also pursue an exponential distribution. The concept of reboot and repairman's vacation are incorporated to make the model more practical and versatile. The expressions for several performance measures such as availability, reliability, and MTTF are obtained with the help of the Markov process. Likewise, sensitivity analysis is done to study the impact of various parameters on system performance measures. The results are explained by taking numerical illustrations. [ABSTRACT FROM AUTHOR]

The mission success probability (MSP) is a critical indicator for phased mission systems (PMSs). In the modern aerospace industry, redundancy techniques, including component/phase redundancy, are commonly seen to increase the MSP of the whole system. These component/phase redundancies make the reliability analysis more complex. Meanwhile, one or more components are required for normal working for different subsystems, called the K/N structure. In this article, a Markov‐process method is proposed for PMS with K/N subsystems and different redundancy strategies. Then, a universal system optimization model is proposed to optimize system structure and redundancy strategies for all subsystems at the same time. Then, an improved genetic algorithm (GA) is used to resolve the optimization problem. At last, a propulsion system is used as an engineering case, showing the proposed binary decision diagram‐based method. [ABSTRACT FROM AUTHOR]

Lyme disease is the most common vector-borne disease in the United States impacting the Northeast and Midwest at the highest rates. Recently, it has become established in southeastern and south-central regions of Canada. In these regions, Lyme disease is caused by Borrelia burgdorferi, which is transmitted to humans by an infected Ixodes scapularis tick. Understanding the parasite-host interaction is critical as the white-footed mouse is one of the most competent reservoir for B. burgdorferi. The cycle of infection is driven by tick larvae feeding on infected mice that molt into infected nymphs and then transmit the disease to another susceptible host such as mice or humans. Lyme disease in humans is generally caused by the bite of an infected nymph. The main aim of this investigation is to study how diapause delays and demographic and seasonal variability in tick births, deaths, and feedings impact the infection dynamics of the tick-mouse cycle. We model tick-mouse dynamics with fixed diapause delays and more realistic Erlang distributed delays through delay and ordinary differential equations (ODEs). To account for demographic and seasonal variability, the ODEs are generalized to a continuous-time Markov chain (CTMC). The basic reproduction number and parameter sensitivity analysis are computed for the ODEs. The CTMC is used to investigate the probability of Lyme disease emergence when ticks and mice are introduced, a few of which are infected. The probability of disease emergence is highly dependent on the time and the infected species introduced. Infected mice introduced during the summer season result in the highest probability of disease emergence. [ABSTRACT FROM AUTHOR]

This article explores the concept of environment-induced decoherence in quantum exclusion semigroups. It discusses the structure and properties of the decoherence-free algebra and its relationship with the set of fixed points. The authors provide mathematical descriptions and proofs for the properties they describe. The paper serves as a mathematical model for open quantum systems and provides conditions for the occurrence of environment-induced decoherence. The research is supported by the National Natural Science Foundation of China. [Extracted from the article]

In this paper, a multistage reciprocating compressor system is considered to study, analyze and improve its reliability by incorporating the redundancies using Markov approach. In Markov method, the reliability is assessed by creating state space model and deriving probabilistic equations of all the states. The developed equations are further solved with the help of a MATLAB. Constant failure and repair rates are considered for the different components in the system. Standby redundancy has been employed to enhance the system reliability. System reliability value for the basic system model, i.e. Model 1 at 10,000 h is 0.1252 that has been increased by using standby redundancies in Model 4 with no repair to 0.6428 and with repair to 0.9374. This work will be helpful to the manufacturers, users, researchers and others by the application, and implementation of the proposed methodology. [ABSTRACT FROM AUTHOR]

High-altitude platforms (HAPs) are considered to be the most important equipment for next-generation wireless communication technologies. In this paper, we investigate the channel characteristics under the configurations of massive multiple-input multiple-output (MIMO) space and large bandwidth at millimeter-wave (mmWave) bands, along with the moving essence of the HAP and ground terminals. A non-stationary three-dimensional (3D) geometry-based stochastic model (GBSM) is proposed for a HAP communication system. We use a cylinder-based geometric modeling method to construct the channel and derive the channel impulse response (CIR). Additionally, the birth–death process of the scatterers is enclosed using the Markov process. Large-scale parameters such as free space loss and rainfall attenuation are also taken into consideration. Due to the relative motion between HAP and ground terminals, the massive MIMO space, and the wide bandwidth in the mmWave band, the channel characteristics of HAP exhibit non-stationarities in time, space, and frequency domains. By deriving the temporal auto-correlation function (ACF), we explore the non-stationarity in the time domain and the impact of various parameters on the correlations across the HAP-MIMO channels. The spatial cross-correlation function (CCF) for massive MIMO scenarios, and the frequency correlation function (FCF) in the mmWave bands are also considered. Moreover, we conduct simulation research using MATLAB. Simulation results show that the theoretical results align well with the simulation results, and this highlights the fact that the constructed 3D GBSM can characterize the non-stationary characteristics of HAP-MIMO channels across the time, space, and frequency domains. [ABSTRACT FROM AUTHOR]

To achieve the model construction and strategy selection of carbon emissions under the constraints of limited data information, this study explores the inherent laws underlying the evolution of different population models from the perspective of natural population growth, obstructive population changes constrained by environmental and other conditions, population changes considering age structure and population development in the form of partial differential equations on the basis of systematic analysis of population factors and their impact on changes in social environment and material level, then an equivalent substitution function is obtained according to the homotopy transformation idea in topology, so that the problem can be dealt with in a unified way. The results show that the extended STIRPAT model has a better fitting effect, and using Markov process to reverse adjust and correct the influencing factor which is predicted by population evolution model before yields more accurate prediction results. The idea of analyzing carbon emissions based on population changes also provides an effective method for dealing with related problems. [ABSTRACT FROM AUTHOR]

Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal river profiles and similarity of geometries at scales greater than approximately 100km highlight relatively simple emergent properties. A general challenge then, addressed in this manuscript, is development of a theory of landscape evolution that embraces such scale-dependent insights. We do so by incorporating randomness and probability into a theory of fluvial erosion. First, we explore the use of stochastic differential equations of the Langevin type, and the Fokker--Planck equation, for predicting migration of erosional fronts. Second, analytical approaches incorporating distributions of driving forces, critical thresholds and associated proxies are developed. Finally, a linear programming approach is introduced, that, at its core, treats evolution of longitudinal profiles as a Markovian stochastic problem. The theory is developed essentially from first principles and incorporates physics governing fluvial erosion. We explore predictions of this theory, including the natural growth of discontinuities and scale-dependent evolution, including local complexity and emergent simplicity. [ABSTRACT FROM AUTHOR]

To ensure the correctness of train control system design and development, the ways of simulation, test and formalization were compared. According to the safe critical attribute of train control system, the characters related to system safety were propounded such as real time, hybrid, distribution (concurrence) and reactivity, and the specific formal methods associated with every character were introduced in details. The analysis and classification of the methods were done based on their mathematical basis and applications, and their advantages and disadvantages were given.Analysis result indicates that every method has determinate limitations, which is determined by the essences of model checking and theory proving. It is pointed out that the presentation of new method, the expansion of existing methods and the integration of many methods will be the development trend of formalization in train control system. [ABSTRACT FROM AUTHOR]

In this paper, we establish a version of the central limit theorem for Markov–Feller continuous time processes (with a Polish state space) that are exponentially ergodic in the bounded-Lipschitz distance and enjoy a continuous form of the Foster–Lyapunov condition. As an example, we verify the assumptions of our main result for a specific piecewise-deterministic Markov process, whose deterministic component evolves according to continuous semiflows, switched randomly at the jump times of a Poisson process. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Markovian regime-switching regression model, which is a graphical model based on the hidden Markov model. This model can be viewed as a clustered regression model, in which a Markov process models the transition from one cluster to another. These clusters are indeed the hidden states of the process, in the hidden Markov model, which are assumed to be a Markov process of order one. Besides, other assumptions of the hidden Markov model are assumed in this model, while the emission distribution is assumed to be the conditional distribution of the response given the covariates and the states. As an application of this model, the problem of prediction of PM 2.5 pollution in Tehran's air based on temperature and pressure during 2015-2017 using the Markovian regime-switching non-parametric additive transitive model, is considered and studied. Furthermore, the package hhsmm in R software, is introduced as a powerful tool for modeling the stated model.1. IntroductionState-switching models are models in which the distribution of a sequence of observations (usually during a time interval) is controlled by a sequence of hidden states, such that the conditional distribution of observations given each state is different from that given others. Hidden Markov and semi-Markov Models [27] are the most common instances of state-switching models, in which the hidden state is a Markov or semi-Markov process. Some other models, including the regime-switching models or Kalman-Filter model, are in this category. Various applications of such models are introduced by the researchers including, speech recognition [12], cognitive learning [24], brain performance modeling [15], modeling environmental processes [4, 5, 6], sequential analysis, reliability theory [7], biological analysis [8, 9, 27], and many other applications.2. Main ResultsA hidden Markov model is constructed by the following items: (1) Transition Probability Matrix $\pmb{\Gamma} =(\gamma_{ij})$, where\begin{equation*}\gamma_{ij}=\Pr(S_{t+1}=j|S_t=i), i,j=1,\ldots,J,\end{equation*}such that\begin{equation*}\sum_{i=1}^{J}{\gamma_{ij}}=1, j=1,\ldots,J.\end{equation*} (2) Initial State Probability $ \pmb{\delta}=(\delta_j) $, where\begin{equation*}\delta_j=\Pr(S_1=j), j=1,\ldots,J; \sum_{j=1}^{J}{\delta_j}=1.\end{equation*} (3) Observation distributions $ f_1(y),\ldots,f_J(y) $, where$$ f_j(y)=\Pr(Y_t=y | S_t=j); j=1,\ldots,J,$$which are also called state-dependent distribution or emission distribution. When $ y_t $ is a continuous random variable, $ f_j(y) $ is a probability density function, which is usually a normal distribution or mixture of normal distributions.The regime-switching regression model is introduced by [14] as follows:(2.1) $$ y_{t} = x_{t}^T \beta_{s_t} + \sigma_{s_t}\epsilon_t,$$in which $\{y_t\}$ is the sequence of responses, $\{x_t\}$ is the sequence of covariates, $\{\epsilon_t\}$ are sequence of (usually) i.i.d. normally distributed errors with zero mean and a variance equal to 1, and $\beta_{s_t}$ and $\sigma_{s_t}$ are the regression coefficients and the standard deviation of errors at state $s_t$, respectively. A generalization of the model (2.1) to the the additive regime-switching regression model is introduced by [20] as follows:(2.2) $$y_{t} = \mu_{s_t} + \sum_{j=1}^p f_{j,s_t}(x_{j,t}) + \sigma_{s_t}\epsilon_t,$$Letting $x_t = (y_{t-\ell},\ldots,y_{t-L}, z_{t-\ell},\ldots,z_{t-L})$, for lags $L > \ell \geq 1$ in (2.2), the non-parametric additive transitive regime-switching regression model is obtained. All models in this paper and all necessary tools for modeling, initialization, fitting, and prediction of these models are included in the R package hhsmm, which can be downloaded from https://cran.r-project.org/package=hhsmm. The reader is also referred to [3] for more information and examples about hhsmm package. 3. Summary of Proofs/ConclusionsThe data set for this paper is obtained from two sources. The AQI data set (PM2.5 values) are obtained from https://airnow.tehran.ir/, while the air temperature and pressure are obtained from Iran meteorological organization. Figure 3, shows the time-series plots of this data set. To visualize the additive regime-switching regression model, we first consider only the temperature as the covariate in the model. Figure 4, presents the prediction of PM2.5 in Tehran city air using a nonparametric additive regime-switching regression model, only based on the air temperature, in each of the four hidden states. The points in each state are colored by different colors and the curve of the prediction is drawn with the same color. As one can see from this figure, the predictive curves are fairly fitted to the points in each state. As a competitor model, we consider the single-state additive regression model. Figure 5, presents the result of the comparison of prediction precision of PM2.5 in Tehran city air, using two fitted models: the regime-switching regression model with four hidden states and the single state non-parametric additive regression model. The mean squared error in each model is presented in each plot. One can see that the non-parametric additive regime-switching regression model with four hidden states performs better than the single-state non-parametric additive regression model. Another introduced model is the additive transitive regime-switching regression model. Figure 6, shows the result of the prediction of PM2.5 in Tehran city air using a transitive regime switching non-parametric additive regression model with a 1-day lag. The mean squared error of the model is presented in the plot. One can see that this model performs better than the two other competitors. Finally, the additive transitive regime-switching model is used for the prediction of the future values of PM2.5. Figure 7, presents the out-of-sample prediction of PM2.5 in Tehran city air using a transitive regime switching non-parametric additive regression model with 10 days lag. The mean squared error of the model is equal to 99.3. The result of the prediction is satisfactory.

The main purpose of this study is to examine the behavior of certain industrial systems under the conditions of product warranty policy. Given this policy, we are interested in considering all the parameters of the system in order to study them and show their impact on the proposed system. In order to increase the efficiency of the system and activate the product warranty policy, the system will undergo a preliminary examination for any system failure occurrence to determine the reasons that led to the failure. After completing the initial inspection, the mechanic will decide whether it is a user-caused failure or a manufacturing defect to determine whether or not the repair of the broken appliance is covered by the manufacturer’s contractual warranty policy. All times in the system are assumed as a negative exponential distribution. The expressions for some measures of system effectiveness such as reliability, mean time to system failure (MTSF), and availability are derived using the supplementary variable technique and Laplace transform. Sensitivity analysis and a relative sensitivity are then carried out in order to recognize how each system parameter affects performance measures. Finally, some numerical examples are designed and performed to show how the change of each system parameter affects system performance.