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This Special Issue (SI), titled "Probability Theory and Stochastic Modeling with Applications", is concerned with the theory and applications of stochastic models. Footnotes 1 B Disclaimer/Publisher's Note: b The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). It consists of sixteen papers, and we would like to thank all the authors for their positive answers to our call for papers for the SI, as well as for their efforts to provide a high-quality contribution. Using fuzzy variables and robust optimization, the authors provide the electricity transaction policy under different expected costs so that the expectation of the risk-averse distribution system operator is fulfilled. [Extracted from the article]

This paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing random variations in the economic and financial environments. We prove a sufficient condition on the distribution of jumps of the business process ensuring the smoothness of the ruin probability as a function of the initial capital and obtain for this function an integro-differential equation. [ABSTRACT FROM AUTHOR]

In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. Markov chains are given by a classical transition function that generates a pair of conjugate linear Markov operators in a Banach space of measurable bounded functions and in a Banach space of bounded finitely additive measures. We study sequences of Cesaro means of powers of Markov operators on the set of finitely additive probability measures. It is proved that the set of all limit measures (points) of such sequences in the weak topology generated by the preconjugate space is non-empty, weakly compact, and all of them are invariant for this operator. We also show that the well-known Doeblin condition (D) for the ergodicity of a Markov chain is equivalent to condition (∗) : all invariant finitely additive measures of the Markov chain are countably additive, i.e., there are no invariant purely finitely additive measures. We give all the proofs for the most general case. [ABSTRACT FROM AUTHOR]

A ring oscillator is a well-known circuit used for generating random numbers, and interested readers can find many research results concerning the evaluation of the randomness with a packaged test suit. However, the authors think there is room for evaluating the unpredictability of a sequence from another viewpoint. In this paper, the authors focus on Wold's RO-based generator and propose a statistical test to numerically evaluate the randomness of the RO-based generator. The test adopts the state transition probabilities in a Markov process and is designed to check the uniformity of the probabilities based on hypothesis testing. As a result, it is found that the RO-based generator yields a biased output from the viewpoint of the transition probability if the number of ROs is small. More precisely, the transitions 01 → 01 and 11 → 11 happen frequently when the number l of ROs is less than or equal to 10. In this sense, l > 10 is recommended for use in any application, though a packaged test suit is passed. Thus, the authors believe that the proposed test contributes to evaluating the unpredictability of a sequence when used together with available statistical test suits, such as NIST SP800-22. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a multi-server queueing system with a marked Markov arrival process of two types of customers and a phase-type distribution of service time depending on the type of customer. Customers of both types are assumed to be impatient and renege from the buffers after an exponentially distributed number of times. The strategy of flexible provisioning of priorities is analyzed. It assumes a randomized choice of the customers from the buffers, with probabilities dependent on the relation between the number of customers in a priority finite buffer and the fixed threshold value. To simplify the construction of the underlying Markov chain and the derivation of the explicit form of its generator, we use the so-called generalized phase-type distribution. It is shown that the created Markov chain fits the category of asymptotically quasi-Toeplitz Markov chains. Using this fact, we show that the considered Markov chain is ergodic for any value of the system parameters and compute its stationary distribution. Expressions for key performance measures are presented. Numerical results that show how the parameters of the control strategy affect the system's performance measurements are given. It is shown that the results can be used for managerial purposes and that it is crucial to take correlation in the arrival process into account. [ABSTRACT FROM AUTHOR]

From the initial development of probability theory to the present days, the convergence of various discrete processes to simpler continuous distributions remains at the heart of stochastic analysis. Many efforts have been devoted to functional central limit theorems (also referred to as the invariance principle), dealing with the convergence of random walks to Brownian motion. Though quite a lot of work has been conducted on the rates of convergence of the weighted sums of independent and identically distributed random variables to stable laws, the present paper is the first to supply the rates of convergence in the functional limit theorem for stable subordinators. On the other hand, there is a lot of activity on the convergence of CTRWs (continuous time random walks) to processes with memory (subordinated Markov process) described by fractional PDEs. Our second main result is the first one yielding rates of convergence in such a setting. Since CTRW approximations may be used for numeric solutions of fractional equations, we obtain, as a direct consequence of our results, the estimates for error terms in such numeric schemes. [ABSTRACT FROM AUTHOR]

This Special Issue is devoted to probability, statistics, stochastic processes, and their different applications in systems and networks analysis. Risks are considered as the antipotential of the system development, which are the retarders of the reproduction rate of the system. The system optimization process requires computation time because if the system contains k components, each with three service modes, 3k service configurations need to be estimated. Multi-server mass service systems (compared to well-designed single-server systems) are more complex and more difficult to handle, especially when the arrival time distribution is arbitrary. [Extracted from the article]

Content-centric vehicular networks (CCVNs) have considered distributed proactive caching as an attractive approach for the timely provision of emerging services. The naïve caching schemes cache all of the contents to only one selected roadside unit (RSU) for requested vehicles to decrease the data acquisition delay between the data source and the vehicles. Due to the high deployment cost for RSUs and their limited capacity of caching, the vehicular networks could support only a limited number of vehicles and a limited amount of content and thus decrease the cache hit ratio. This paper proposes a mobility-aware distributed proactive caching protocol (MDPC) in CCVNs. MDPC caches contents to the selected RSUs according to the movement of vehicles. To reduce the redundancy and the burden of caching for each RSU, MDPC distributes to cache partial contents by the movement pattern, the probability to predict the next locations (RSUs) on the Markov model based on the current RSU. For recovery of prediction failures, MDPC allows each RSU to request partial missing contents to relatively closer neighbor RSUs with a short delay. Next, we expand the protocol with traffic optimization called MDPC_TO to minimize the amount of traffic for achieving proactive caching in CCVNs. In proportion to the mobility probability of a vehicle toward each of the next RSUs, MDPC_TO controls the amount of pre-cached contents in each of the next RSUs. Then, MDPC_TO has constraints to provide enough content from other next RSUs through backhaul links to remove the delay due to prediction failures. Simulation results verify that MDPC_TO produces less traffic than MDPC. [ABSTRACT FROM AUTHOR]

The stochastic process non-homogeneous Markov system in a stochastic environment in continuous time (S-NHMSC) is introduced in the present paper. The ordinary non-homogeneous Markov process is a very special case of an S-NHMSC. I studied the expected population structure of the S-NHMSC, the first central classical problem of finding the conditions under which the asymptotic behavior of the expected population structure exists and the second central problem of finding which expected relative population structures are possible limiting ones, provided that the limiting vector of input probabilities into the population is controlled. Finally, the rate of convergence was studied. [ABSTRACT FROM AUTHOR]

In this paper we study a mobility-aware call admission control algorithm in a mobile hotspot. To this end, a vehicle is considered which has an access point with a fixed capacity. The vehicle alternates between stop and moving phases. When the vehicle is in the stop phase, it services new and handover calls by prioritizing them via a probabilistic bandwidth reservation (BR) policy. Based on this policy, new handover calls may enter the reservation space with a predefined probability. When the vehicle is in the moving phase, it services new calls only. In that phase, two different policies are considered: (a) the classical complete sharing (CS) policy, where new calls are accepted in the system whenever there exists available bandwidth, and (b) the probabilistic BR policy. Depending on the selected policy in the moving phase, we propose the probabilistic BR loss model (if the CS policy is selected) and the generalized probabilistic BR loss model (if the probabilistic BR policy is selected). In both stop and moving phases, where the call arrival process is Poisson, calls require a single bandwidth unit in order to be accepted in the system, while the service time is exponentially distributed. To analytically determine call blocking probabilities and the system’s utilization, we propose efficient iterative algorithms based on two-dimensional Markov chains. The accuracy of the proposed algorithms is verified via simulation. [ABSTRACT FROM AUTHOR]

A practical probabilistic data association filter is proposed for tracking multiple targets in clutter. The number of joint data association events increases combinatorially with the number of measurements and the number of targets, which may become computationally impractical for even small numbers of closely located targets in real target-tracking applications in heavily cluttered environments. In this paper, a Markov chain model is proposed to generate a set of feasible joint events (FJEs) for multiple target tracking that is used to approximate the multi-target data association probabilities and the probabilities of target existence of joint integrated probabilistic data association (JIPDA). A Markov chain with the transition probabilities obtained from the integrated probabilistic data association (IPDA) for single-target tracking is designed to generate a random sequence composed of the predetermined number of FJEs without incurring additional computational cost. The FJEs generated are adjusted for the multi-target tracking environment. A computationally tractable set of these random sequences is utilized to evaluate the track-to-measurement association probabilities such that the computational burden is substantially reduced compared to the JIPDA algorithm. By a series of simulations, the track confirmation rates and target retention statistics of the proposed algorithm are compared with the other existing algorithms including JIPDA to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We propose a method for fitting transition intensities to a sufficiently large set of trajectories of a continuous-time non-homogeneous Markov chain with a finite state space. Starting with simulated data computed with Gompertz–Makeham transition intensities, we apply the proposed method to fit piecewise linear intensities and then compare the transition probabilities corresponding to both the Gompertz–Makeham transition intensities and the fitted piecewise linear intensities; the main comparison result is that the order of magnitude of the average fitting error per unit time—chosen as a year—is always less than 1%, thus validating the methodology proposed. [ABSTRACT FROM AUTHOR]

We analyze the role of hedge fund, swap dealer, and arbitrageur activity in the crude oil market. The contribution of our work is to examine the role of institutional traders in switching between high-volatility and low-volatility regimes. Using confidential position data on institutional investors, we first analyze the linkages between trader positions and fundamentals. We find that these institutional position changes reflect fundamental economic factors. Subsequently, we adopt a Markov regime-switching model with time-varying probabilities and find that institutional position changes contribute incrementally to the probability of regime changes. [ABSTRACT FROM AUTHOR]

To optimally plan maintenance of wind turbine blades, knowledge of the degradation processes and the remaining useful life is essential. In this paper, a method is proposed for calibration of a Markov deterioration model based on past inspection data for a range of blades, and updating of the model for a specific wind turbine blade, whenever information is available from inspections and/or condition monitoring. Dynamic Bayesian networks are used to obtain probabilities of inspection outcomes for a maximum likelihood estimation of the transition probabilities in the Markov model, and are used again when updating the model for a specific blade using observations. The method is illustrated using indicative data from a database containing data from inspections of wind turbine blades. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the notion of the "minus logarithm of stationary probability" as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a deterministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems. [ABSTRACT FROM AUTHOR]

We consider the following generalization of the classical coupon collector problem. We assume that, in addition to the initial collection of standard coupons, there is one more coupon that acts as a reset button, removing all coupons from the part of the collection that has already been drawn. For the case where standard coupons have unequal probabilities of being drawn, we obtain the distribution of the waiting time until the end of the collection process. For the case where standard coupons have equal probabilities, we derive a simple formula for the expected waiting time in terms of the beta function, and discuss the asymptotic properties of this expected waiting time, when the number of standard coupons tends toward infinity. [ABSTRACT FROM AUTHOR]

In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the stability of finite-dimensional distribution of time-inhomogeneous, discrete-time Markov chains on a general state space. The main result of the paper provides an estimate for the absolute difference of finite-dimensional distributions of a given time-inhomogeneous Markov chain and its perturbed version. By perturbation, we mean here small changes in the transition probabilities. Stability estimates are obtained using the coupling method. [ABSTRACT FROM AUTHOR]

The stochastic nature of the thickness of boride layers formed on carbon steel is described in this paper. Additionally, the probability distribution of the layer thickness is studied to determine the best-fit probability distribution. The study combines the use of an empirical model (power-law) and the Markov chain principles, with the purpose of demonstrating that it is feasible to develop a model that represents the non-uniformity of the thickness of boride layers that form on carbon steel. The results indicate that the mean and variance tend to increase when the time or temperature is increased. The findings of this paper demonstrate that an analytical solution to the Kolmogorov's system differential equation can adequately represent the behavior of non-uniform boride layer formed on low-carbon steel, regardless of the temperature or duration of treatment. [ABSTRACT FROM AUTHOR]

Performance analysis and design space exploration of bufferless Networks-on-Chip is done mainly through time-consuming cycle-accurate simulation, due to the chaotic nature of packet deflections, which have thus far prevented the development of an accurate analytical model. In order to raise the level of abstraction as well as capture the inherently probabilistic behavior of deflection routing, this paper presents a methodology for employing Markov chain models in the analysis of the behavior of bufferless Networks-on-Chip. A formal way of describing a bufferless NoC topology as a set of discrete-time Markov chains is presented. It is demonstrated that by combining this description with the network average distance, it is possible to obtain the expectation of the number of hops between any pair of nodes in the network as a function of the flit deflection probability. Comparisons between the proposed model and cycle-accurate simulation demonstrate the accuracy achieved by the model, with negligible computational cost. The useful range of the proposed model is quantified, demonstrating that it has an error of less than 10% for a significant proportion (between 33 and 75%) of the injection rate range below saturation. Finally, a simple equation for comparing mesh topologies with a "back-of-the-envelope" calculation is introduced. [ABSTRACT FROM AUTHOR]

A hidden Markov model (HMM) is a useful tool for modeling dependent heterogeneous phenomena. It can be used to find factors that affect real-world events, even when those factors cannot be directly observed. HMMs differ from traditional methods by using state variables and mixture distributions to model the hidden states. This allows HMMs to find relationships between variables even when the variables cannot be directly observed. HMM can be extended, allowing the transition probabilities to depend on covariates. This makes HMMs more flexible and powerful, as they can be used to model a wider range of sequential data. Modeling covariates in a hidden Markov model is particularly difficult when the dimension of the state variable is large. To avoid these difficulties, Markovian properties are achieved by implanting the previous state variables to the logistic regression model. We apply the proposed method to find the factors that affect the hidden state of matsutake mushroom growth, in which it is hard to find covariates that directly affect matsutake mushroom growth in Korea. We believe that this method can be used to identify factors that are difficult to find using traditional methods. [ABSTRACT FROM AUTHOR]

This research focuses on exploring various techniques and models for simulating the random behavior of energy facilities or systems. These simulations are essential in identifying the likelihood of component failures within the studied facilities. By assessing the potential consequences of emergency scenarios, this analysis serves as a fundamental aspect of synthesizing and analyzing reliability in the cyber-physical system. Ultimately, the study aims to enhance the management and control of reliability and safety for these facilities. In this study, a unified heating source is considered as an energy facility (as part of district heating systems), for example, a combined heat and power plant. However, the developed methods and models have sufficient universality for their adaptation to other energy facilities without significant changes. The research methodology is based on the use of Markov random processes and laws of the probability theory. The basic model of the energy facilities is formulated for the conditions of the simplest events flow with appropriate assumptions and constraints, in particular, ordinary events and independence of events (failures and restorations). To take into account the non-ordinary events (failures) and dependences between some failures, corresponding modifications of the basic model are proposed. A computational experiment was carried out using the developed models, and graphical interpretations of the results are presented. The obtained results allow us to formulate some preliminary conclusions about the range of influence of the simulated factors on the reliability analysis of studied facilities and to outline conditions and areas of their admissible application. [ABSTRACT FROM AUTHOR]

In the framework of coding theory, under the assumption of a Markov process (X t) on a finite alphabet A , the compressed representation of the data will be composed of a description of the model used to code the data and the encoded data. Given the model, the Huffman's algorithm is optimal for the number of bits needed to encode the data. On the other hand, modeling (X t) through a Partition Markov Model (PMM) promotes a reduction in the number of transition probabilities needed to define the model. This paper shows how the use of Huffman code with a PMM reduces the number of bits needed in this process. We prove the estimation of a PMM allows for estimating the entropy of (X t) , providing an estimator of the minimum expected codeword length per symbol. We show the efficiency of the new methodology on a simulation study and, through a real problem of compression of DNA sequences of SARS-CoV-2, obtaining in the real data at least a reduction of 10.4%. [ABSTRACT FROM AUTHOR]

The paper is devoted to the investigation of the distributed proof generation process, which makes use of recursive zk-SNARKs. Such distributed proof generation, where recursive zk-SNARK-proofs are organized in perfect Mercle trees, was for the first time proposed in Latus consensus protocol for zk-SNARKs-based sidechains. We consider two models of a such proof generation process: the simplified one, where all proofs are independent (like one level of tree), and its natural generation, where proofs are organized in partially ordered set (poset), according to tree structure. Using discrete Markov chains for modeling of corresponding proof generation process, we obtained the recurrent formulas for the expectation and variance of the number of steps needed to generate a certain number of independent proofs by a given number of provers. We asymptotically represent the expectation as a function of the one variable n / m , where n is the number of provers m is the number of proofs (leaves of tree). Using results obtained, we give numerical recommendation about the number of transactions, which should be included in the current block, idepending on the network parameters, such as time slot duration, number of provers, time needed for proof generation, etc. [ABSTRACT FROM AUTHOR]

This short paper concerns the analysis of the M/M/k queueing system with customer abandonment. In this system, service managers provide a finite buffer space, which is a waiting area that prevents customers from abandoning the system. Abandonment of the system can occur from reneging (exiting from the queue while waiting), and/or balking (leaving the system without waiting). We derive an analytical expression to represent the impact of the buffer space capacity on the delay probability and the abandonment probability for a system with deferred abandonment. The result indicates the provision of the buffer space in a large system could only increase the delay probability while the abandonment probability remains unchanged. Despite the benevolent intentions of service managers, providing a buffer space may exacerbate the performance of larger systems. [ABSTRACT FROM AUTHOR]

We consider the computing issues of the steady probabilities for block-structured discrete-time Markov chains that are of upper-Hessenberg or lower-Hessenberg transition kernels with a continuous phase set. An effective computational framework is proposed based on the wavelet transform, which extends and modifies the arguments in the literature for quasi-birth-death (QBD) processes. A numerical procedure is developed for computing the steady probabilities based on the fast discrete wavelet transform, and several examples are presented to illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

We present REGA, a new adaptive-sampling-based algorithm for the control of finite-horizon Markov decision processes (MDPs) with very large state spaces and small action spaces. We apply a variant of the ϵ -greedy multiarmed bandit algorithm to each stage of the MDP in a recursive manner, thus computing an estimation of the "reward-to-go" value at each stage of the MDP. We provide a finite-time analysis of REGA. In particular, we provide a bound on the probability that the approximation error exceeds a given threshold, where the bound is given in terms of the number of samples collected at each stage of the MDP. We empirically compare REGA against another sampling-based algorithm called RASA by running simulations against the SysAdmin benchmark problem with 2 10 states. The results show that REGA and RASA achieved similar performance. Moreover, REGA and RASA empirically outperformed an implementation of the algorithm that uses the "original" ϵ -greedy algorithm that commonly appears in the literature. [ABSTRACT FROM AUTHOR]

As multimedia traffic has been increasing and is expected to grow more sharply, various technologies using caches have been attracting lots of attention. As one breakthrough technology to deal with the explosively growing traffic, exclusive OR (XOR)-based index coding has been widely investigated because it can greatly enhance the efficiency of network resource by reducing the number of transmissions. In this paper, we investigate how to apply XOR-based index coding to large-scaled practical streaming systems for video traffic that accounts for more than 70% of total Internet traffic. Contrary to most previous studies that have focused on theoretical analysis of optimal performance or development of optimal index coding schemes, our study proposes a new XOR coding-based video streaming (XC). We also propose a new grouping algorithm for creating XC groups while guaranteeing the complete backward compatibility of XC with existing streaming schemes such as unicast (UC), multicast (MC), and broadcast (BC). The performance of the proposed scheme is analyzed in two steps. First, the behavior of video contents in caches at clients is modeled as a Markov chain, and the steady-state probabilities and caching probabilities for each piece of video content are derived. Based on the probabilities, the performance of the proposed system is then analyzed in terms of the average number of connections that each client requires in order to receive one video content. Our numerical results show that the proposed video streaming scheme using XC can reduce the average number of transmissions by up to 18%, compared to the conventional scheme. [ABSTRACT FROM AUTHOR]

The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns. [ABSTRACT FROM AUTHOR]

Event recognition in smart spaces is an important and challenging task. Most existing approaches for event recognition purely employ either logical methods that do not handle uncertainty, or probabilistic methods that can hardly manage the representation of structured information. To overcome these limitations, especially in the situation where the uncertainty of sensing data is dynamically changing over the time, we propose a multi-level information fusion model for sensing data and contextual information, and also present a corresponding method to handle uncertainty for event recognition based on Markov logic networks (MLNs) which combine the expressivity of first order logic (FOL) and the uncertainty disposal of probabilistic graphical models (PGMs). Then we put forward an algorithm for updating formula weights in MLNs to deal with data dynamics. Experiments on two datasets from different scenarios are conducted to evaluate the proposed approach. The results show that our approach (i) provides an effective way to recognize events by using the fusion of uncertain data and contextual information based on MLNs and (ii) outperforms the original MLNs-based method in dealing with dynamic data. [ABSTRACT FROM AUTHOR]

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new "Markov chain dockless bike-sharing fleet size solution" algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing. [ABSTRACT FROM AUTHOR]

To solve the conflict when multi-user packets are transmitted in a shared wireless link, a novel frameless slotted-ALOHA protocol is proposed. Signature codes are used to help the receiver identify the set of transmitting users, and successive interference cancellation technology is employed to recover conflicting packets. Thus, the information in the conflicting slot can be reused to reduce the number of retransmissions. Taking the number of backlogged users in each slot as a system state, a Markov chain model is established to analyze the protocol, in which the state transition probabilities are obtained based on the binomial distribution of packets sent in a slot. Under the maximum number of detectable conflicting users, the best value is taken, traffic balance equations are obtained, and the expressions of throughput, average number of backlogged users, average successful transmission probability and average memory size are derived. Finally, a numerical simulation is carried out to accurately analyze the influence of the first transmission probability of the packets on various performance indexes and the effectiveness of the theoretical analysis is further verified by the simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative, modified Kullback–Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the 'optimal' value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain. [ABSTRACT FROM AUTHOR]

This paper compares two approaches to analyzing longitudinal discrete-time binary outcomes. Dynamic binary response models focus on state occupancy and typically specify low-order Markovian state dependence. Multi-spell duration models focus on transitions between states and typically allow for state-specific duration dependence. We show that the former implicitly impose strong and testable restrictions on the transition probabilities. In a case study of poverty transitions, we show that these restrictions are severely rejected against the more flexible multi-spell duration models. [ABSTRACT FROM AUTHOR]

The analysis of self-stabilizing algorithms is often limited to the worst case stabilization time starting from an arbitrary state, i.e., a state resulting from a sequence of faults. Considering the fact that these algorithms are intended to provide fault tolerance in the long run, this is not the most relevant metric. A common situation is that a running system is an a legitimate state when hit by a single fault. This event has a much higher probability than multiple concurrent faults. Therefore, the worst case time to recover from a single fault is more relevant than the recovery time from a large number of faults. This paper presents techniques to derive upper bounds for the mean time to recover from a single fault for self-stabilizing algorithms based on Markov chains in combination with lumping. To illustrate the applicability of the techniques they are applied to a new self-stabilizing coloring algorithm. [ABSTRACT FROM AUTHOR]

In password guessing, the Markov model is still widely used due to its simple structure and fast inference speed. However, the Markov model based on random sampling to generate passwords has the problem of a high repetition rate, which leads to a low cover rate. The model based on enumeration has a lower cover rate for high-probability passwords, and it is a deterministic algorithm that always generates the same passwords in the same order, making it vulnerable to attack. We design a dynamic distribution mechanism based on the random sampling method. This mechanism enables the probability distribution of passwords to be dynamically adjusted and tend toward uniform distribution strictly during the generation process. We apply the dynamic distribution mechanism to the Markov model and propose a dynamic Markov model. Through comparative experiments on the RockYou dataset, we set the optimal adjustment degree α. Compared with the Markov model without the dynamic distribution mechanism, the dynamic Markov model reduced the repetition rate from 75.88% to 66.50% and increased the cover rate from 37.65% to 43.49%. In addition, the dynamic Markov model had the highest cover rate for high-probability passwords. Finally, the model avoided the lack of a deterministic algorithm, and when it was run five times, it reached almost the same cover rate as OMEN. [ABSTRACT FROM AUTHOR]

This research aims to determine the existence of inflection points when companies' credit risk goes from being minimal (Hedge) to being high (Ponzi). We propose an analysis methodology that determines the probability of hedge credits to migrate to speculative and then to Ponzi, through simulations with homogeneous Markov chains and the k-means clustering method to determine thresholds and migration among clusters. To prove this, we used quarterly financial data from a sample of 35 public enterprises over the period between 1 July 2006 and 28 March 2020 (companies listed on the USA, Mexico, Brazil, and Chile stock markets). For simplicity, we make the assumption of no revolving credits for the companies and that they face their next payment only with their operating cash flow. We found that Ponzi companies (1) have a 0.79 probability average of default, while speculative ones had (0) 0.28, and hedge companies (−1) 0.009, which are the inflections point we were looking for. Our work's main limitation lies in not considering the entities' behavior when granting credits in altered states (credit relaxation due to credit supply excess). [ABSTRACT FROM AUTHOR]

Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications. [ABSTRACT FROM AUTHOR]

The problem of stabilizing the spreading process to a prescribed probability distribution over a complex network is considered, where the dynamics of the nodes in the network is given by discrete-time Markov-chain processes. Conditions for the positioning and identification of actuators and sensors are provided, and sufficient conditions for the exponential stability of the desired distribution are derived. Simulations results for a network of N = 106 corroborate our theoretical findings. [ABSTRACT FROM AUTHOR]

This study investigated the uncertainty of the multistage assembly process from the viewpoint of a stream of defects in the product assembly process. The vulnerable spots were analyzed and the fluctuations were controlled during this process. An uncertainty evaluation model was developed for the assembly process on the basis of an object-oriented Petri net (OOPN) by replacing its transition function with a fitted defect changing function. The definition of entropy in physics was applied to characterize the uncertainty of the model in evaluating the assembly process. The uncertainty was then measured as the entropy of the semi-Markov chain, which could be used to calculate the uncertainty of a specific subset of places, as well as the entire process. The OOPN model could correspond to the Markov process because its reachable token can be directly mapped to the Markov process. Using the steady-state probability combined with the uncertainty evaluation, the vulnerable spots in the assembly process were identified and a scanning test program was proposed to improve the quality of the assembly process. Finally, this work analyzed the assembly process on the basis of the uncertainty of the assembly structure and the variables of the assembly process. Finally, the case of a certain product assembly process was analyzed to test the advantages of this method. [ABSTRACT FROM AUTHOR]

We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call i-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore, we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the i-entities in small example systems as a first sanity check and find that i-entities largely fulfil simple expectations. [ABSTRACT FROM AUTHOR]

The scarcity of water resources in mountain areas can distort normal water application patterns with among other effects, a negative impact on water supply and river ecosystems. Knowing the probability of droughts might help to optimize a priori the planning and management of the water resources in general and of the Andean watersheds in particular. This study compares Markov chain- (MC) and Bayesian network- (BN) based models in drought forecasting using a recently developed drought index with respect to their capability to characterize different drought severity states. The copula functions were used to solve the BNs and the ranked probability skill score (RPSS) to evaluate the performance of the models. Monthly rainfall and streamflow data of the Chulco River basin, located in Southern Ecuador, were used to assess the performance of both approaches. Global evaluation results revealed that the MC-based models predict better wet and dry periods, and BN-based models generate slightly more accurately forecasts of the most severe droughts. However, evaluation of monthly results reveals that, for each month of the hydrological year, either the MC- or BN-based model provides better forecasts. The presented approach could be of assistance to water managers to ensure that timely decision-making on drought response is undertaken. [ABSTRACT FROM AUTHOR]

When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which allows the quantification of the specific properties of process models. These characteristics are, for instance, complexity, comprehensibility, cohesion, and uncertainty. This work is focused on defining a method that allows us to measure the uncertainty of a process model, which was modelled by using stochastic Petri nets (SPN). The principle of this method consists of mapping of all reachable marking of SPN into the continuous-time Markov chain and then calculating its stationary probabilities. The uncertainty is then measured as the entropy of the Markov chain (it is possible to calculate the uncertainty of the specific subset of places as well as of whole net). Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy against maximum entropy (the resulting value is normalized to the interval <0,1>). The calculated entropy can also be used as a measure of the model complexity. [ABSTRACT FROM AUTHOR]

We develop ideas proposed by Van der Straeten to extend maximum entropy principles to Markov chains. We focus in particular on the convergence of such estimates in order to explain how our approach makes possible the estimation of transition probabilities when only short samples are available, which opens the way to applications to non-stationary processes. The current work complements an earlier communication by providing numerical details, as well as a full derivation of the multi-constraint two-state and three-state maximum entropy transition matrices. [ABSTRACT FROM AUTHOR]

A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers' self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the M A P on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided. [ABSTRACT FROM AUTHOR]

The reliability and cost-effectiveness of energy conversion in gas turbine systems are strongly dependent on an accurate diagnosis of possible process and sensor anomalies. Because data collected from a gas turbine system for diagnosis are inherently uncertain due to measurement noise and errors, probabilistic methods offer a promising tool for this problem. In particular, dynamic Bayesian networks present numerous advantages. In this work, two Bayesian networks were developed for compressor fouling and turbine erosion diagnostics. Different prior probability distributions were compared to determine the benefits of a dynamic, first-order hierarchical Markov model over a static prior probability and one dependent only on time. The influence of data uncertainty and scatter was analyzed by testing the diagnostics models on simulated fleet data. It was shown that the condition-based hierarchical model resulted in the best accuracy, and the benefit was more significant for data with higher overlap between states (i.e., for compressor fouling). The improvement with the proposed dynamic Bayesian network was 8 percentage points (in classification accuracy) for compressor fouling and 5 points for turbine erosion compared with the static network. [ABSTRACT FROM AUTHOR]

Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries. [ABSTRACT FROM AUTHOR]

For a G -inhomogeneous semi-Markov chain and G -inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G -inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G -inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds. [ABSTRACT FROM AUTHOR]

In the nervous system, information is conveyed by sequence of action potentials, called spikes-trains. As MacKay and McCulloch suggested, spike-trains can be represented as bits sequences coming from Information Sources ( I S ). Previously, we studied relations between spikes' Information Transmission Rates (I T R) and their correlations, and frequencies. Now, I concentrate on the problem of how spikes fluctuations affect I T R . The I S are typically modeled as stationary stochastic processes, which I consider here as two-state Markov processes. As a spike-trains' fluctuation measure, I assume the standard deviation σ , which measures the average fluctuation of spikes around the average spike frequency. I found that the character of I T R and signal fluctuations relation strongly depends on the parameter s being a sum of transitions probabilities from a no spike state to spike state. The estimate of the Information Transmission Rate was found by expressions depending on the values of signal fluctuations and parameter s. It turned out that for smaller s < 1 , the quotient I T R σ has a maximum and can tend to zero depending on transition probabilities, while for 1 < s , the I T R σ is separated from 0. Additionally, it was also shown that I T R quotient by variance behaves in a completely different way. Similar behavior was observed when classical Shannon entropy terms in the Markov entropy formula are replaced by their approximation with polynomials. My results suggest that in a noisier environment (1 < s) , to get appropriate reliability and efficiency of transmission, I S with higher tendency of transition from the no spike to spike state should be applied. Such selection of appropriate parameters plays an important role in designing learning mechanisms to obtain networks with higher performance. [ABSTRACT FROM AUTHOR]