Discrete and Continuous Models and Applied Computational Science最新文献_第5页

Performance analysis of queueing system model under priority scheduling algorithms within 5G networks slicing framework 5G网络切片框架下优先级调度算法下排队系统模型的性能分析

Discrete and Continuous Models and Applied Computational Science Pub Date : 2022-02-25 DOI: 10.22363/2658-4670-2022-30-1-5-20

K. Y. Adou, E. Markova, Elena A. Zhbankova

引用次数: 0

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging 具有多次休假、拒绝和背弃变量的马尔可夫多服务器反馈队列的数学分析

Discrete and Continuous Models and Applied Computational Science Pub Date : 2022-02-25 DOI: 10.22363/2658-4670-2022-30-1-21-38

A. Bouchentouf, Latifa Medjahri, Mohamed Boualem, Ajay Kumar

{"title":"Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging","authors":"A. Bouchentouf, Latifa Medjahri, Mohamed Boualem, Ajay Kumar","doi":"10.22363/2658-4670-2022-30-1-21-38","DOIUrl":"https://doi.org/10.22363/2658-4670-2022-30-1-21-38","url":null,"abstract":"In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47910011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Quantum mereology in finite quantum mechanics 有限量子力学中的量子表象

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-12-15 DOI: 10.22363/2658-4670-2021-29-4-347-360

V. Kornyak

引用次数: 1

On involutive division on monoids 一元群上的对合除法

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-12-15 DOI: 10.22363/2658-4670-2021-29-4-387-398

O. K. Kroytor, M. Malykh

{"title":"On involutive division on monoids","authors":"O. K. Kroytor, M. Malykh","doi":"10.22363/2658-4670-2021-29-4-387-398","DOIUrl":"https://doi.org/10.22363/2658-4670-2021-29-4-387-398","url":null,"abstract":"We consider an arbitrary monoid MM, on which an involutive division is introduced, and the set of all its finite subsets SetMM. Division is considered as a mapping d:SetMM{d:SetM times M}, whose image d(U,m){d(U,m)} is the set of divisors of mm in UU. The properties of division and involutive division are defined axiomatically. Involutive division was introduced in accordance with the definition of involutive monomial division, introduced by V.P. Gerdt and Yu.A. Blinkov. New notation is proposed that provides brief but explicit allowance for the dependence of division on the SetMM element. The theory of involutive completion (closures) of sets is presented for arbitrary monoids, necessary and sufficient conditions for completeness (closedness) - for monoids generated by a finite set XX. The analogy between this theory and the theory of completely continuous operators is emphasized. In the last section, we discuss the possibility of solving the problem of replenishing a given set by successively expanding the original domain and its connection with the axioms used in the definition of division. All results are illustrated with examples of Thomas monomial division.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41255236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

In Memory of Vladimir Gerdt 纪念弗拉基米尔·格特

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-12-15 DOI: 10.22363/2658-4670-2021-29-4-306-336

V. Edneral

引用次数: 0

Towards the analysis of the performance measures of heterogeneous networks by means of two-phase queuing systems 基于两阶段排队系统的异构网络性能分析

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-09-30 DOI: 10.22363/2658-4670-2021-29-3-242-250

T. V. Rykova

{"title":"Towards the analysis of the performance measures of heterogeneous networks by means of two-phase queuing systems","authors":"T. V. Rykova","doi":"10.22363/2658-4670-2021-29-3-242-250","DOIUrl":"https://doi.org/10.22363/2658-4670-2021-29-3-242-250","url":null,"abstract":"Due to a multistage nature of transmission processes in heterogeneous 4G, 5G mobile networks, multiphase queuing systems become one of the most suitable ways for the resource allocation algorithms analysis and network investigation. In this paper, a few scientific papers that approached heterogeneous networks modelling by means of multiphase queuing systems are reviewed, mentioning the difficulties that arise with this type of analytical analysis. Moreover, several previously investigated models are introduced briefly as an example of two-phase systems of finite capacity and a special structure in discrete time that can be used for analysing resource allocation schemes based on the main performance measures obtained for wireless heterogeneous networks. One of the model presents a two-phase tandem queue with a group arrival flow of requests and a second phase of the complex structure that consists of parallel finite queues. The second model is a two-phase tandem queue with Markov modulated geometric arrival and service processes at the first phase and exhaustive service process at the second phase, which solves a cross-layer adaption problem in a heterogeneous network.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46351217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Evaluation of firewall performance when ranging a filtration rule set 对过滤规则集进行排序时的防火墙性能评估

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-09-30 DOI: 10.22363/2658-4670-2021-29-3-230-241

Anatoly Y. Botvinko, K. Samouylov

{"title":"Evaluation of firewall performance when ranging a filtration rule set","authors":"Anatoly Y. Botvinko, K. Samouylov","doi":"10.22363/2658-4670-2021-29-3-230-241","DOIUrl":"https://doi.org/10.22363/2658-4670-2021-29-3-230-241","url":null,"abstract":"This article is a continuation of a number of works devoted to evaluation of probabilistic-temporal characteristics of firewalls when ranging a filtration rule set. This work considers a problem of the decrease in the information flow filtering efficiency. The problem emerged due to the use of a sequential scheme for checking the compliance of packets with the rules, as well as due to heterogeneity and variability of network traffic. The order of rules is non-optimal, and this, in the high-dimensional list, significantly influences the firewall performance and also may cause a considerable time delay and variation in values of packet service time, which is essentially important for the stable functioning of multimedia protocols. One of the ways to prevent decrease in the performance is to range a rule set according to the characteristics of the incoming information flows. In this work, the problems to be solved are: determination and analysis of an average filtering time for the traffic of main transmitting networks; and assessing the effectiveness of ranging the rules. A method for ranging a filtration rule set is proposed, and a queuing system with a complex request service discipline is built. A certain order is used to describe how requests are processed in the system. This order includes the execution of operations with incoming packets and the logical structure of filtration rule set. These are the elements of information flow processing in the firewall. Such level of detailing is not complete, but it is sufficient for creating a model. The QS characteristics are obtained with the help of simulation modelling methods in the Simulink environment of the matrix computing system MATLAB. Based on the analysis of the results obtained, we made conclusions about the possibility of increasing the firewall performance by ranging the filtration rules for those traffic scripts that are close to real ones.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44224953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymptotically accurate error estimates of exponential convergence for the trapezoidal rule 梯形规则指数收敛的渐近精确误差估计

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-09-30 DOI: 10.22363/2658-4670-2021-29-3-251-259

A. Belov, V. S. Khokhlachev

{"title":"Asymptotically accurate error estimates of exponential convergence for the trapezoidal rule","authors":"A. Belov, V. S. Khokhlachev","doi":"10.22363/2658-4670-2021-29-3-251-259","DOIUrl":"https://doi.org/10.22363/2658-4670-2021-29-3-251-259","url":null,"abstract":"In many applied problems, efficient calculation of quadratures with high accuracy is required. The examples are: calculation of special functions of mathematical physics, calculation of Fourier coefficients of a given function, Fourier and Laplace transformations, numerical solution of integral equations, solution of boundary value problems for partial differential equations in integral form, etc. For grid calculation of quadratures, the trapezoidal, the mean and the Simpson methods are usually used. Commonly, the error of these methods depends quadratically on the grid step, and a large number of steps are required to obtain good accuracy. However, there are some cases when the error of the trapezoidal method depends on the step value not quadratically, but exponentially. Such cases are integral of a periodic function over the full period and the integral over the entire real axis of a function that decreases rapidly enough at infinity. If the integrand has poles of the first order on the complex plane, then the Trefethen-Weidemann majorant accuracy estimates are valid for such quadratures. In the present paper, new error estimates of exponentially converging quadratures from periodic functions over the full period are constructed. The integrand function can have an arbitrary number of poles of an integer order on the complex plane. If the grid is sufficiently detailed, i.e., it resolves the profile of the integrand function, then the proposed estimates are not majorant, but asymptotically sharp. Extrapolating, i.e., excluding this error from the numerical quadrature, it is possible to calculate the integrals of these classes with the accuracy of rounding errors already on extremely coarse grids containing only 10 steps.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47840332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Shifted Sobol points and multigrid Monte Carlo simulation 移位Sobol点和多网格蒙特卡罗模拟

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-09-30 DOI: 10.22363/2658-4670-2021-29-3-260-270

A. Belov, Maxim A. Tintul

{"title":"Shifted Sobol points and multigrid Monte Carlo simulation","authors":"A. Belov, Maxim A. Tintul","doi":"10.22363/2658-4670-2021-29-3-260-270","DOIUrl":"https://doi.org/10.22363/2658-4670-2021-29-3-260-270","url":null,"abstract":"Multidimensional integrals arise in many problems of physics. For example, moments of the distribution function in the problems of transport of various particles (photons, neutrons, etc.) are 6-dimensional integrals. When calculating the coefficients of electrical conductivity and thermal conductivity, scattering integrals arise, the dimension of which is equal to 12. There are also problems with a significantly large number of variables. The Monte Carlo method is the most effective method for calculating integrals of such a high multiplicity. However, the efficiency of this method strongly depends on the choice of a sequence that simulates a set of random numbers. A large number of pseudo-random number generators are described in the literature. Their quality is checked using a battery of formal tests. However, the simplest visual analysis shows that passing such tests does not guarantee good uniformity of these sequences. The magic Sobol points are the most effective for calculating multidimensional integrals. In this paper, an improvement of these sequences is proposed: the shifted magic Sobol points that provide better uniformity of points distribution in a multidimensional cube. This significantly increases the cubature accuracy. A significant difficulty of the Monte Carlo method is a posteriori confirmation of the actual accuracy. In this paper, we propose a multigrid algorithm that allows one to find the grid value of the integral simultaneously with a statistically reliable accuracy estimate. Previously, such estimates were unknown. Calculations of representative test integrals with a high actual dimension up to 16 are carried out. The multidimensional Weierstrass function, which has no derivative at any point, is chosen as the integrand function. These calculations convincingly show the advantages of the proposed methods.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47562089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Evaluation of the firewall influence on the session initiation by the SIP multimedia protocol 防火墙对SIP多媒体协议发起会话的影响评估

Discrete and Continuous Models and Applied Computational Science Pub Date : 2021-09-30 DOI: 10.22363/2658-4670-2021-29-3-221-229

Anatoly Y. Botvinko, K. Samouylov

{"title":"Evaluation of the firewall influence on the session initiation by the SIP multimedia protocol","authors":"Anatoly Y. Botvinko, K. Samouylov","doi":"10.22363/2658-4670-2021-29-3-221-229","DOIUrl":"https://doi.org/10.22363/2658-4670-2021-29-3-221-229","url":null,"abstract":"Firewalls is one of the major components to provide network security. By using firewalls, you can solve such problems as preventing unauthorized access, and deleting, modifying and/or distributing information under protection. The process of information flows filtration by a firewall introduces additional time delays, thus possibly leading to disruption of stable operation of the protected automated system or to inaccessibility of the services provided by the system. Multimedia services are particularly sensitive to service time delays. The main purpose of the work presented in this paper is to evaluate the influence of the firewall on the time delays in data transmission process in the automated system with multimedia data transmission protocols. The evaluation is provided by the queuing theory methods while a session is initiated between two users by the Session Initiation Protocol (SIP) with firewall message filtration. A firewall is a local or functional distributing tool that provides control over the incoming and/or outgoing information in the automated system (AS), and ensures the protection of the AS by filtering the information, i.e., providing analysis of the information by the criteria set and making a decision on its distribution.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43868796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0