Search Results (51)

In recent years, blockchains have been attracting attention because they are decentralized networks with transparency and trustworthiness. Generally, transactions on blockchain networks with higher transaction fees are processed preferentially compared to others. The processing fee varies significantly depending on other transactions; it is difficult to predict the fee, and it may be significantly high. These are major barriers to blockchain utilization. Although several consensus algorithms have been proposed to solve these problems, their performance has not been fully evaluated. In this study, we model a blockchain system with a base fee, such as in Ethereum, via a priority queueing model. To assess the model’s performance, we derive the stability condition, stationary probability, average number of customers, and average waiting time for each type of customer. In deriving the stability conditions, we propose a method that uses the theoretical values of the partial models. These theoretical values match well with those obtained from Monte Carlo simulations, confirming the validity of the analysis. Full article

The introduction of mechanical energy during a friction process stimulates the system to eliminate this disturbance and find ways for energy dissipation. There are two principal situations: the system is either near equilibrium or far from equilibrium. Near equilibrium, it can be expected that the disturbance will be damped after a certain time, and the system will settle in a stationary state at a level where it began. However, the situation could be entirely different when the system is far from equilibrium. After a phase of instability and crossing a critical parameter, there is a probability of a change in the order level. This means that a new structure will be formed. This paper describes some aspects of the criteria that lead a friction process inside the grease film to instability and examines the influence of different dependencies. In this publication, the dependencies are extended to verify the stability criterion. Finally, the rest phase of a thixotropic experiment is examined from the perspective of potential instability and, thus, the possibility of self-organizing processes occurring. Full article

Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for accepting orders for delivery. The existence of the time lag between order placing and delivery to the pick-up point is accounted for via modeling the order’s processing as the service in the dual tandem queueing system. Distinguishing features of this tandem queue are the account of possible irregularity in order generation via consideration of the versatile Markov arrival process and the possibilities of batch transfer of the orders to the pick-up point, group withdrawal of orders there, and client no-show. To reduce the probability of an order rejection at the pick-up point due to the overflow of the warehouse, a threshold strategy of order admission at the first stage on a tandem is proposed. Under the fixed value of the threshold, tandem operation is described by the continuous-time multidimensional Markov chain with a block lower Hessenberg structure for the generator. Stationary performance measures of the tandem system are calculated. Numerical results highlight the dependence of these measures on the capacity of the warehouse and the admission threshold. The possibility of the use of the results for managerial goals is demonstrated. In particular, the results can be used for the optimal selection of the capacity of a warehouse and the policy of suspending order admission. Full article

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems. Full article

This paper is devoted to the analysis of fluctuations in the solar wind plasma and interplanetary magnetic field parameters observed by Solar Orbiter and WIND spacecraft at different scales ranging from ~10³ to 10⁷ km. We consider two long data intervals where the distances between the spacecraft are 0.1 and 0.5 AU, respectively, and they are located close to the Sun–Earth line. Transformation of the fluctuation’s properties on the way from the Sun to Earth is analyzed for different types of solar wind associated with quasi-stationary and transient solar phenomena. The time series of bulk speed are shown to undergo a slight modification, even for large spacecraft separation, while the time series of the interplanetary magnetic field magnitude and components as well as proton density may be transformed even at a relatively short distance. Though the large-scale solar wind structures propagate the distance up to 0.5 AU without significant change, local structures at smaller scales may be modified. The statistical properties of the fluctuations such as relative standard deviation or probability distribution function and its moments remain nearly unchanged at different distances between the two spacecraft and are likely to depend mostly on the type of the solar wind. Full article

Effective real-time health condition monitoring of the roller table and through shaft bearings in the annealing kiln roller system of glass production lines is crucial for maintaining their operational safety and stability for the quality and production efficiency of glass products. However, the collected vibration signal of the roller bearing system is affected by the low rotating frequency and strong mechanical background noise, which shows the width impact interval and non-stationary multi-component characteristics. Moreover, the distribution characteristics of monitoring data and probability of fault occurrence of the roller bearing and through shaft bearing improve the difficulty of the fault diagnosis and condition monitoring of the annealing kiln roller system, as well as the reliance on professional experience and prior knowledge. Therefore, this paper proposes a variable-scale attention mechanism guided time-frequency feature fusion transfer learning method for a bearing fault diagnosis at different installation positions in an annealing kiln roller system. Firstly, the instinct time decomposition method and the Gini–Kurtosis composed index are used to decompose and reconstruct the signal for noise reduction, wavelet transform with the Morlet basic function is used to extract the time-frequency features, and histogram equalization is introduced to reform the time-frequency map for the blur and implicit time-frequency features. Secondly, a variable-scale attention mechanism guided time-frequency feature fusion framework is established to extract multiscale time-dependency features from the time-frequency representation for the distinguished fault diagnosis of roller table bearings. Then, for through shaft bearings, the vibration signal of the roller table bearing is used as the source domain and the signal of the through shaft bearing is used as the target domain, based on the feature fusion framework and the multi-kernel maximum mean differences metric function, and the transfer diagnosis method is proposed to reduce the distribution differences and extract the across-domain invariant feature to diagnose the through shaft bearing fault speed under different working conditions, using a small sample. Finally, the effectiveness of the proposed method is verified based on the vibration signal from the experimental platform and the roller bearing system of the glass production line. Results show that the proposed method can effectively diagnose roller table and through shaft bearings’ fault information in the annealing kiln roller system. Full article

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’. Full article

We consider an irreducible positive-recurrent discrete-time Markov process on the state space $X={\mathbb{Z}}_{+}^M\times J$, where ${\mathbb{Z}}_{+}$ is the set of non-negative integers and $J=\{1,2,\dots ,n\}$. The number of states in $J$ may be either finite or infinite. We assume that the process is a homogeneous quasi-birth-and-death process (QBD). It means that the one-step transition probability between non-boundary states $(k,i)$ and $(n,j)$ may depend on $i,j$, and $n-k$ but not on the specific values of $k$ and $n$. It is shown that the stationary probability vector of the process is expressed through square matrices of order $n$, which are the minimal non-negative solutions to nonlinear matrix equations. Full article

6G will connect heterogeneous intelligent agents to make them natively operate complex cooperative tasks. When connecting intelligence, two main research questions arise to identify how artificial intelligence and machine learning models behave depending on (i) their input data quality, affected by errors induced by interference and additive noise during wireless communication; (ii) their contextual effectiveness and resilience to interpret and exploit the meaning behind the data. Both questions are within the realm of semantic and goal-oriented communications. With this paper, we investigate how to effectively share communication spectrum resources between a legacy communication system (i.e., data-oriented) and a new goal-oriented edge intelligence one. Specifically, we address the scenario of an enhanced Mobile Broadband (eMBB) service, i.e., a user uploading a video stream to a radio access point, interfering with an edge inference system, in which a user uploads images to a Mobile Edge Host that runs a classification task. Our objective is to achieve, through cooperation, the highest eMBB service data rate, subject to a targeted goal effectiveness of the edge inference service, namely the probability of confident inference on time. We first formalize a general definition of a goal in the context of wireless communications. This includes the goal effectiveness, (i.e., the goal achievability rate, or the probability of achieving the goal), as well as goal cost (i.e., the network resource consumption needed to achieve the goal with target effectiveness). We argue and show, through numerical evaluations, that communication reliability and goal effectiveness are not straightforwardly linked. Then, after a performance evaluation aiming to clarify the difference between communication performance and goal effectiveness, a long-term optimization problem is formulated and solved via Lyapunov stochastic network optimization tools to guarantee the desired target performance. Finally, our numerical results assess the advantages of the proposed optimization and the superiority of the goal-oriented strategy against baseline 5G-compliant legacy approaches, under both stationary and non-stationary communication (and computation) environments. Full article

In this paper, we consider a multi-server queue with a finite buffer. Request arrivals are defined by the Markov arrival process. Service is provided to groups of requests. The minimal and maximal group sizes are fixed. The service time of a group has a phase-type distribution with an irreducible representation depending on the size of the group. The requests are impatient. The patience time for an arbitrary request has an exponential distribution. After this time expires, the request is lost if all servers are busy or, if some server is idle, with a certain probability, all requests staying in the buffer start their service even if their number is below the required minimum. The behavior of the system is described by a multi-dimensional continuous-time Markov chain that does not belong to the class of level-independent quasi-birth-and-death processes. The algorithm for the computation of the stationary distribution of this chain is presented, and expressions for the computation of the queuing system’s performance characteristics are derived. The description of a delivery system operation in terms of the analyzed queuing model is given, and the problem of the optimization of its operation is numerically solved. Multi-server queues with a phase-type distribution for the group service time that are dependent on the size of the group, the account of request impatience, and the correlated arrival process have not previously been analyzed in the existing literature. However, they represent a precise model of many real-world objects, including delivery systems. Full article

A queuing system having two different servers is under study. Demands enter the system according to a Markov arrival process. Service times have phase-type distribution. Service of demands is possible only if the fixed number of energy units, probably different for two servers, is available in the system at the potential service beginning moment. Energy units arrive in the system also according to a Markov arrival process and are stored in a stock (battery) of a finite capacity. Leakage of energy units from the stock can occur. Demands waiting in the infinite buffer are impatient and can leave the buffer after an exponentially distributed waiting time. One server is the main one and permanently provides service when the buffer is not empty and the required number of energy units is available. The second server is the assistant server and is switched on or off depending on the availability of energy units and queue length according to the hysteresis strategy defined by two thresholds. The assistant server is switched on when the queue length is not less than the greater threshold and is switched off when the queue length becomes smaller than the smaller threshold. The use of the assistant server has to be paid. Thus, the problem of the optimal selection of the thresholds defining the control strategy naturally arises. To solve this problem, the study of the behavior of the system under any fixed values of the parameters of the control strategy is necessary. Such a study is given in this paper. Numerical results are presented. They illustrate the feasibility of computer realization of the developed algorithms for computation of the stationary distribution of the system states and the main key performance indicators as well as the result of solving one of the possible optimization tasks. Full article

The microalga Dunaliella salina can produce antioxidants such as glutathione, which is an essential and powerful regulator of major cell functions. Changes in the glutathione concentration occur due to a microalga’s response to oxidative stress, which usually occurs when cells are exposed to environmental stressors or reach senescence. This study represents one of the few examples where changes in the glutathione concentration were tracked over the entire growth cycle of an alga. We found significant differences in the glutathione concentration depending on the growth stage. During the early lag growth phase, D. salina had relatively low levels of glutathione (190–280 µmol/10¹² cell), which gradually increased as it entered the log phase (280–500 µmol/10¹² cell) but then decreased as it entered the stationary phase (320–370 µmol/10¹² cell). We also observed that the ratio between the reduced form of glutathione (GSH) and the oxidized form (GSSG) decreased with time, probably as a result of senescence or a lack of nutrients. Full article

Increasing interest has been shown in the subject of non-additive entropic forms during recent years, which has essentially been due to their potential applications in the area of complex systems. Based on the fact that a given entropic form should depend only on a set of probabilities, its time evolution is directly related to the evolution of these probabilities. In the present work, we discuss some basic aspects related to non-additive entropies considering their time evolution in the cases of continuous and discrete probabilities, for which nonlinear forms of Fokker–Planck and master equations are considered, respectively. For continuous probabilities, we discuss an H-theorem, which is proven by connecting functionals that appear in a nonlinear Fokker–Planck equation with a general entropic form. This theorem ensures that the stationary-state solution of the Fokker–Planck equation coincides with the equilibrium solution that emerges from the extremization of the entropic form. At equilibrium, we show that a Carnot cycle holds for a general entropic form under standard thermodynamic requirements. In the case of discrete probabilities, we also prove an H-theorem considering the time evolution of probabilities described by a master equation. The stationary-state solution that comes from the master equation is shown to coincide with the equilibrium solution that emerges from the extremization of the entropic form. For this case, we also discuss how the third law of thermodynamics applies to equilibrium non-additive entropic forms in general. The physical consequences related to the fact that the equilibrium-state distributions, which are obtained from the corresponding evolution equations (for both continuous and discrete probabilities), coincide with those obtained from the extremization of the entropic form, the restrictions for the validity of a Carnot cycle, and an appropriate formulation of the third law of thermodynamics for general entropic forms are discussed. Full article

Next-generation wireless communication networks are expected to offer extremely high data rates supported by very low latency and radically new applications, which require a new wireless radio technology paradigm. However, it is crucial to assist the radio link over the fast varying and highly dynamic channel to satisfy the diverse requirements of next-generation wireless networks. Recently, communication via autonomous electric vertical takeoff and landing (eVTOL) has gained momentum, owing to its potential for cost-effective network deployment. It is considered one of the most promising technologies conceived to support smart radio terminals. However, to provide efficient and reliable communications between ground base stations and eVTOLs as well as between eVTOLs and other eVTOLs, realistic eVTOL channel models are indispensable. In this paper, we propose a nonstationary geometry-based stochastic channel model for eVTOL communication links. The proposed eVTOL channel model framework considers time-domain nonstationarity and arbitrary eVTOL trajectory and is sufficiently general to support versatile C bands. One of the critical challenges for eVTOL is the fast vertical takeoff and landing flight patterns affecting the regular propagation communication channel. Moreover, we present a new method for estimating the SNR over the non-stationary fast dynamic time-variant eVTOL channel by utilizing the sliding window adaptive filtering technique. Furthermore, we present an information–theoretic approach to characterize the end-to-end transmission delay over the eVTOL channel and prove that the optimal transmission scheme strongly depends upon the eVTOL link configuration. In addition, to analyze the occurrence of deep fade regions in eVTOL links, we analyze the outage probability, which is an important performance metric for wireless channels operating over dynamic fading channels, and make an important observation that the outage probability increases non-linearly with the eVTOL height. Furthermore, we consider the commercially available eVTOL specifications and data to validate the channel model and analyze the Doppler shift and latency for the exponential acceleration and exponential deceleration velocities profiles during the takeoff and landing operation. This paper provides a new and practical approach for the design, optimization, and performance evaluation of future eVTOL-assisted next-generation wireless communications. Full article

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. Full article