Stationary Analysis Fluid Model Driven by an Queue

This article examines an system with catastrophic server failures and repairs that feeds a fluid queue. The buffer content's stationary distribution function is expressed explicitly in terms of confluent queueing hyper geometric functions. The expression for the joint probability of the buffer's content and the number of customers in an queueing system has been obtained using continued fraction techniques. The stationary analyses of fluid flow queueing models in a stochastic environment can be effectively scrutinized and applied in the modern telecommunication systems and various advanced computer communication networks. Especially, the fluid queues are used in the performance analyses of data packet transmission networks, traffic flows at high-speed computer networks, and rechargeable batteries in smart mobile phones. A few key performance indicators are acquired. Finally, the numerical work is shown to show how the buffer content distribution behaves and how the performance metrics for the suggested fluid queueing system work.

We consider a tandem fluid system composed of multiple buffers connected in a series. The first buffer receives input from a number of independent homogeneous on-off sources and each buffer provides input to the next buffer. The active (on) periods and silent (off) periods follow general and exponential distribution, respectively. Furthermore, the generally distributed active periods are controlled by an exponential timer. Under this assumption, explicit expressions for the distribution of the buffer content for the first buffer fed by a single source is obtained for the fluid queue driven by discouraged arrivals queue and infinite server queue. The buffer content distribution of the subsequent buffers when the first buffer is fed by multiple sources are found in terms of confluent hypergeometric functions. Numerical results are illustrated to compare the trend of the average buffer content for the models under consideration.

Dispersion modeling at urban intersections

Editorial: "Cyber Security Prevention, Defenses Driven by AI and Mathematical Modelling and Simulation Tools". The rise of the Smart Computation driven by the Artificial Intelligence with the ubiquitous access to Data Computer Communication Technologies and Internet by anyone, from anywhere at any time, has become a working, learning and socializing platform for people worldwide and if often known as Cyberspace. The past century technological advancements in the Data Communications Technologies , Semiconductor Industry (SI) and a Very Large Scale Integration (VLSI) contributed to significant increase of computer systems performance and computational capacity of small portable computers and cell phones that have become available at low cost for people anywhere in the world. Due to relatively low cost, anyone and anywhere in the world may purchase a PC, Laptop, Smart Phone, or Tablet. These smart-computational devices are capable of powerful computation and connecting almost any computer system in the world via Internet 24/7. Given the current unstable geopolitical ecosystem in conjunction with the dynamic development in the artificial intelligence (AI), smart computation and fast Internet with the ubiquitous access to Internet 24/7, the reliable and secure provision of confidentiality, integrity and accessibility of data available via Internet, has become essential for government, business, the industry and individual worldwide. The fast developments in the field of AI gave rise to a new era of smart computation that can easily be utilized by the governments, special groups or very well trained and skilled individual with malicious intend due to their political , economic or personal motivation. Given the rise of next generation of smart cyberattacks, the use of AI and Mathematical Modeling and Simulations Tools has become essential part of cybersecurity tool kit, to make sure that contra cyber measures are most effective and reliable in real-time 24/7. The Research Topic was received with great interest in the scholastic and professional community worldwide. The paper selection was very competitive based on rigorous reviews presenting seven papers. The Research Topic presents a collection of selected peer reviewed papers presenting most recent advances and the state-of-the-art in the field of. Applied AI and Mathematical Modelling in Cyber Security. The papers show evidence that cyberattacks are becoming much more sophisticated, computationally complex, and challenging for the current cyber security mechanisms, which drives the research, innovation, and development of the next generation of AI assisted Cyber Security imbedded with the Mathematical Modelling and Simulations tools. The first paper presents practical application of eXplainable AI (XAI) in cybersecurity while enabling a machine-human interaction. The second paper discusses effective use of AI applied in the cyberattacks prevention utilizing Intrusion Detection and Prevention Systems (IDPS). The third paper presents use of deep learning and machine learning algorithms to identify the malicious malware. The fourth paper discusses the use of encryption and cryptographic algorithms in creating an effective cyber defenses in the Internet of Thing Cyber Infrastructures. The fifth paper presents effective methods to identify possible cyberattacks utilizing the noisy audio evidence. The sixth paper illustrates utilization of simulation based on the dropout mechanisms to identify obfuscated malicious traffic. The seventh paper presents effective applications of Generative AI Influenced Spread, Extended Models and Awareness Spread Models to analyze fake news propagation and enable the intervention strategy assessment. The Research Topic brings to light most recent developments in the field of applied AI and Mathematical Modeling and Simulations in Cyber Security, while presenting current and future challenges presented by ongoing challenges in the field of studies. Given the current dynamic advancements in the field of AI, Smart Computation and AI, we are yet at the very beginning of new era of new generation of ultra-smart and most sophisticated cyberattacks that will require a new ultra-smart cyber defenses to make sure that the future cyberspace will be safe, reliable and beneficial to the betterment of mankind for future generations for many years to come. The Research Topic promotes creation of the AI Inspired Cyber Security Center, bringing together multidisciplinary research teams working together while seeking best solutions and mechanism to make the current and future cyberspace safe, secure and reliable 27/7 in the nation and worldwide. The Topic Editors would like to use this opportunity to express most sincere gratitude to contributors, reviewers, to Dr. Enrique Morillas, Dr. Nicola Zannone, Mr Sean O'Reilly Ms Alice Gooch, and Colleagues at Frontiers in Computer Science for their strong support, kind guidance and good counsel provided during the course of the project.

We consider a feedback fluid queue with a finite buffer and downward jumps, where the net flow rate and the jump size for the buffer content are controlled by a background Markov chain with a finite state space. The feedback means that the transition structure of the background Markov chain may change when the buffer content becomes empty or full. In this chapter, we show that the loss rate for this fluid queue decays exponentially as the buffer size gets large under a negative drift condition.

The paper gives models and analytic techniques for addressing critical issues of the Broadband Integrated Services Digital Network which will use the Asynchronous Transfer Mode. The traffic is expected to be highly bursty and variable at the source and consequently a key issue is admission control. We study a 4-parameter device called a regulator which acts as a policing device as well as a traffic shaper. The device is a generalized leaky bucket with a data buffer, a token buffer supplied by a constant-rate token stream, and a peak rate controller; the outputs of the device are streams of priority and marked cells. The composite system comprising of the source and the regulator is represented in a stochastic fluid model since fluid flow has been found to have properties well matched to the ATM environment, and the Markov Modulated Fluid Source allows bursty characteristics to be accurately modelled. A complete procedure based on spectral expansions for calculating the system's stationary state distribution is given. It is shown that with proper design the regulator effectively controls a three-way trade-off between throughput, delay and burstiness. Numerical results reveal that performance is sensitive to source characteristics such as the squared coefficient of variation of burst and silent periods. The second part of the paper characterizes the output of the regulator. The distributions of the time periods spent in the various states by the output process are calculated exactly. From this an approximate Markovian characterization is obtained. The output streams of priority and marked cells are coupled to capture their correlations. For the simple case of two-state on-off sources, the approximate Markovian characterization of the regulator's output rate processes is explicitly given and it is distinguished by the property that all moments are identical to those of the actual processes. With this characterization an original goal of analyzing a composite system of access regulation and statistical multiplexing is separated, decomposed and thereby made tractable.

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L ; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L ) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L .

A fluid queue with ON periods arriving according to a Poisson process and having a long-tailed distribution has long range dependence. As a result, its performance deteriorates. The extent of this performance deterioration depends on a quantity determined by the average values of the system parameters. In the case when the the performance deterioration is the most extreme, we quantify it by studying the time until the amount of work in the system causes an overflow of a large buffer. This turns out to be strongly related to the tail behavior of the increase in the buffer content during a busy period of the M/G/\infty queue feeding the buffer. A large deviation approach provides a powerful method of studying such tail behavior.

The reduction in the duration of the development of new vehicles and the associated desire to reduce the costs of automotive plants contribute to a more active application of mathematical modeling to solve engineering problems. The tasks, which are analyzing and predicting the fatigue life of vehicle components and assemblies, can be solved using a set of methods and tools of mathematical modeling.
 This article discusses the development of a complex of mathematical models of the front and rear suspensions of a passenger automobile, which have the properties necessary for accurate reproduction of wheel loads and dynamic behavior of the suspension as a mechanical system. The complex of mathematical models is implemented in a multi-link modeling environment. The models are designed to carry out a subsequent validation study of the loading of individual suspension components during forced service life tests. In the future, this complex of mathematical models can be used for simulation of semi-natural forced resource tests of the suspension module, as well as a sample for the development of suspension models of other automobiles.
 The purpose of this work is to form sufficient requirements for mathematical models for the implementation of fatigue durability studies using mathematical modeling methods and obtaining reliable calculation results. Research engineers will be able to follow these requirements to determine and collect initial data for the development of their own mathematical models.

Distributed algorithms such as CSMA provide a popular mechanism for sharing the transmission medium among competing users in large-scale wireless networks. Conventional models for CSMA that are amenable for analysis assume that users always have packets to transmit. In contrast, when users do not compete for medium access when their buffers are empty, a complex interaction arises between the activity states and the buffer contents. We develop a meanfield approach to investigate this dynamic interaction for networks with many users. We identify a time-scale separation between the evolution of the activity states and the buffer contents, and obtain a deterministic dynamical system describing the network dynamics on a macroscopic scale. The fixed point of the dynamical system yields highly accurate approximations for the stationary distribution of the buffer contents and packet delay, even when the number of users is relatively moderate.

Based on a successful conference, the 2022 International Conference on Applied Mathematics and Digital Simulation, AMDS 2022, held virtually via Zoom from November 26-28th, 2022 in Beijing, due to the continuing impact of COVID-19, the contributions are the results of submissions from the conference participants. They provide readers with a broader view of mathematical, statistical and computational science methods, ideas and tools.There are 88 participants in AMDS 2022 online conference, in which the program includes 4 keynote reports (35 minutes), 38 oral presentations (12 mins+3 Q&A) included in two sessions (advances in mathematical modelling and theory, mathematical modelling and computation in engineering and physical sciences) and 10 E-posts. This conference emphasizes the development of theories and applications and promotes interdisciplinary endeavours among mathematicians, statisticians, scientists, engineers and researchers from other disciplines.This volume comprises select proceedings of AMDS 2022 of 48 papers from 75 submissions. All accepted manuscripts were peer-reviewed by 2 reviewers at least in a double-blind review process. A total of 51 reviewers participated in this conference, who provided their professional and strict comments for authors to ensure the topic and quality of the manuscripts. There are eight topic partitions, including mathematical modelling and theory, statistical modelling and data analysis, fluid dynamics and mechanics, intelligent control, machine learning, medical physics, mathematical modelling physical engineering, and optics and engineering. This proceeding constitutes an up-to-date account of principles, techniques, and tools for mathematical simulation & modelling in a wide range of research fields.List of Scientific Committee is available in this Pdf.

We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. Although saturated buffer scenarios have been widely investigated and yield useful throughput estimates for persistent sessions, they fail to capture the fluctuations in buffer contents over time and provide no insight in the delay performance of flows with intermittent packet arrivals. Motivated by that issue, we explore in the present paper random-access networks with buffer dynamics, where flows with empty buffers refrain from competition for the medium. The occurrence of empty buffers thus results in a complex dynamic interaction between activity states and buffer contents, which severely complicates the performance analysis. Hence, we focus on a many-sources regime where the total number of nodes grows large, which not only offers mathematical tractability but is also highly relevant with the densification of wireless networks as the Internet of Things emerges. We exploit timescale separation properties to prove that the properly scaled buffer occupancy process converges to the solution of a deterministic initial value problem and establish the existence and uniqueness of the associated fixed point. This approach simplifies the performance analysis of networks with huge numbers of nodes to a low-dimensional fixed-point calculation. For the case of a complete interference graph, we demonstrate asymptotic stability, provide a simple closed form expression for the fixed point, and prove interchange of the mean-field and steady-state limits. This yields asymptotically exact approximations for key performance metrics, in particular the stationary buffer content and packet delay distributions.

On the reversibility of manufacturing networks

1. Introduction. Mathematical modelling tools are being applied at an increasing rate to the problems arising in the area of combustion. Engineering modelling on full scale combustors is a complex subject typically encompassing chemistry, fluid mechanics (including turbulence effects) and certain aspects of chemical engineering. At the other extreme of basic science, the elementary reactions in combustion systems have been studied at the atomic and molecular level using procedures from quantum mechanics. The gulf between the fundamental atomic scale events and the characteristic behavior of macroscopic combustors is enormous. Therefore, problems in this area are typically broken into smaller segments and studied individually for their own merit and understanding. At this time, the goal of truly integrating together fundamental microscopic processes into an overall numerically implemented mathematical model has not been achieved, although enormous strides are being made towards this direction. The present chapter is concerned with a general question that invariably arises at any level in mathematical modelling of combustion processes as well as in other areas. In this regard, the paper will not focus directly on issues of mathematical modelling per se, but rather on the analysis of such modelling efforts. Examples will be drawn from cases involving transport as well as chemistry, but the illustrations will certainly not sample all aspects of mathematical modelling in the combustion field. For the most part, the treatments will focus on macroscopic issues, although some comments about relevant microscopic atomic level events will also be briefly discussed. It is important to keep in mind that the techniques of sensitivity analysis discussed in this chapter are quite general and they have broad applicability in virtually any area of mathematical modelling.Realistic models of combustion processes inherently require numerical simulations due to the complicated and generally nonlinear nature of the physical processes. In order to understand the role of sensitivity analysis associated with such modelling, it is first necessary to appreciate that one may perform modelling without the use of sensitivity analysis but sensitivity analysis may not be done without the performance of modelling. Indeed, all too often modelling is performed without the utilization of sensitivity techniques, and it is the general thesis of this paper that such efforts will invariably fall short of their full utility without the implementation of a sensitivity analysis.

Background. In recent years, modern technical devices have been created so that to use in the practice of treating diabetes mellitus. These are systems for continuous monitoring of glycemia, which is a significant addition to the widely accepted measurements of glucose levels with a glucometer, various infusion systems, which significantly improve the doctor's decision-making process. However, such technical means are quite expensive and inaccessible to a wide range of users. In addition, their use is associated with both adverse reactions when wearing them and with patient compliance issues. In this case an alternative can be using mathematical modeling tools. Objective. The aim of the paper is to prove the possibility of using mathematical modeling to predict the glycemic profile as a certain degree of alternative to a sensor for continuous monitoring of blood glucose levels under conditions of limited irregular measurements. Methods. To solve the problem it is proposed to employ the technology of mathematical modeling. The structure of the model makes it possible to implement the mathematical formalism by analytical formulae. Results. As a result, the insulin-glucose-tolerance test has been developed that allows quantitatively assessing a patient's personal sensitivity to insulin-bolus therapy. We proposed the mathematical model for solving the problem by analytical formulae. Algorithms for identifying model parameters, an algorithm for calculating the insulin dose that compensates for the carbohydrate component in the intended meal, and an algorithm for predicting the daily glycemic profile have been developed. The software-algorithmic structure for the implementation of the mathematical formalism has been developed. Conclusions. The conducted simulation study employing the technology of mathematical modeling makes it possible to evaluate the functioning of the developed procedures at the preclinical stage. The simplicity of calculations using analytical formulae can be a prerequisite for the implementation of the algorithm in portable autonomous special-purpose devices or in smartdata under the Android OS, which is a definite contribution to development of digital diabetology.