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Probability and Stochastic Processes with Applications to Communications, Systems and...
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Probability and Stochastic Processes with Applications to Communications, Systems and Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (22 October 2022) | Viewed by 17493

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Gurami Tsitsiashvili

E-Mail Website
Guest Editor
Institute for Applied Mathematics, Far Eastern Branch of Russian Academy Sciences, 690041 Vladivostok, Russia
Interests: complex systems; mass service system stability; cooperativity in multiple stochastic systems; multiplicative theorems for queueing network
Special Issues, Collections and Topics in MDPI journals
Dr. Alexander Bochkov

E-Mail Website
Guest Editor
Scientific and Technical Complex Research and Design Institute for Information Technology, Signaling and Telecommunications in Railway Transportation – NIIAS, JSC, 107078 Moscow, Russia
Interests: non-stationary processes; risk assessment, analysis, and management; life-support systems; water purification electrochemical systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

This Special Issue is devoted to probability, statistics, stochastic processes, and their different applications in systems and networks analysis. The Special Issue will include works related to the analysis and applications of different queuing models, which begin with general approaches in modeling queuing systems and networks. Large attention will be devoted to the analysis of probabilistic and statistical methods in telecommunication; Asymptotic analysis of queuing networks in the condition of a large load will be considered since original approaches are being developed in the asymptotic analysis of queuing networks in the condition of a large load and in the calculation of distributions in retrial queuing systems. We welcome the considerations of general complex networks and their structures, e.g., in terms of topology and graph theory, mathematical methods and models in smart cities, exclusive statistical methods, such as statistical estimates in bio/ecology, medicine, neural networks, and works that estimate parameters in complex technical systems, etc.

In general, topics include but are not limited to:

  1. General methods in complex networks and their structure analysis;
  2. Mathematical methods and stochastic models in smart cities;
  3. Statistical problems in ecological networks;
  4. Parameter estimation in complex systems;
  5. Analysis and applications of different queuing models;
  6. Polling systems and Jackson networks in random environments;
  7. Probabilistic and stochastic analysis in telecommunication systems;
  8. Risk analysis in complex technical systems.

Prof. Dr. Gurami Tsitsiashvili
Dr. Alexander Bochkov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Probability, statistics, and stochastic processes
  • Complex networks
  • System analysis
  • Queuing models
  • Complex technical systems
  • Risk analysis
  • Reliability analysis
  • Parameter estimation

Published Papers (12 papers)

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Editorial

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4 pages, 163 KiB  
Editorial
Preface to the Special Issue on Probability and Stochastic Processes with Applications to Communications, Systems and Networks
by Alexander Bochkov and Gurami Tsitsiashvili
Mathematics 2022, 10(24), 4665; https://doi.org/10.3390/math10244665 - 09 Dec 2022
Viewed by 839
Abstract
This Special Issue is devoted to probability, statistics, stochastic processes, and their different applications in systems and networks analysis [...] Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)

Research

Jump to: Editorial, Other

16 pages, 1296 KiB  
Article
On Reliability Function of a k-out-of-n System with Decreasing Residual Lifetime of Surviving Components after Their Failures
by Vladimir Rykov, Nika Ivanova, Dmitry Kozyrev and Tatyana Milovanova
Mathematics 2022, 10(22), 4243; https://doi.org/10.3390/math10224243 - 13 Nov 2022
Cited by 4 | Viewed by 1580
Abstract
We consider the reliability function of a k-out-of-n system under conditions that failures of its components lead to an increase in the load on the remaining ones and, consequently, to a change in their residual lifetimes. Development of models able to [...] Read more.
We consider the reliability function of a k-out-of-n system under conditions that failures of its components lead to an increase in the load on the remaining ones and, consequently, to a change in their residual lifetimes. Development of models able to take into account that failures of a system’s components lead to a decrease in the residual lifetime of the surviving ones is of crucial significance in the system reliability enhancement tasks. This paper proposes a novel approach based on the application of order statistics of the system’s components lifetime to model this situation. An algorithm for calculation of the system reliability function and two moments of its uptime has been developed. Numerical study includes sensitivity analysis for special cases of the considered model based on two real-world systems. The results obtained show the sensitivity of system’s reliability characteristics to the shape of lifetime distribution, as well as to the value of its coefficient of variation at a fixed mean. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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22 pages, 821 KiB  
Article
Analytic and Computational Analysis of GI/Ma,b/c Queueing System
by Mohan Chaudhry and Jing Gai
Mathematics 2022, 10(19), 3445; https://doi.org/10.3390/math10193445 - 22 Sep 2022
Cited by 1 | Viewed by 1248
Abstract
Bulk-service queueing systems have been widely applied in many areas in real life. While single-server queueing systems work in some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server queueing systems (compared to well-developed single-server queueing systems) are more complex and harder [...] Read more.
Bulk-service queueing systems have been widely applied in many areas in real life. While single-server queueing systems work in some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server queueing systems (compared to well-developed single-server queueing systems) are more complex and harder to deal with, especially when the inter-arrival time distributions are arbitrary. This paper deals with analytic and computational analyses of queue-length distributions for a complex bulk-service, multi-server queueing system GI/Ma,b/c, wherein inter-arrival times follow an arbitrary distribution, a is the quorum, and b is the capacity of each server; service times follow exponential distributions. The introduction of quorum a further increases the complexity of the model. In view of this, a two-dimensional Markov chain has to be involved. Currently, it appears that this system has not been addressed so far. An elegant analytic closed-form solution and an efficient algorithm to obtain the queue-length distributions at three different epochs, i.e., pre-arrival epoch (p.a.e.), random epoch (r.e.), and post-departure epoch (p.d.e.) are presented, when the servers are in busy and idle states, respectively. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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12 pages, 3950 KiB  
Article
Processing Large Outliers in Arrays of Observations
by Gurami Tsitsiashvili
Mathematics 2022, 10(18), 3399; https://doi.org/10.3390/math10183399 - 19 Sep 2022
Cited by 1 | Viewed by 1000
Abstract
The interest in large or extreme outliers in arrays of empirical information is caused by the wishes of users (with whom the author worked): specialists in medical and zoo geography, mining, the application of meteorology in fishing tasks, etc. The following motives are [...] Read more.
The interest in large or extreme outliers in arrays of empirical information is caused by the wishes of users (with whom the author worked): specialists in medical and zoo geography, mining, the application of meteorology in fishing tasks, etc. The following motives are important for these specialists: the substantial significance of large emissions, the fear of errors in the study of large emissions by standard and previously used methods, the speed of information processing and the ease of interpretation of the results obtained. To meet these requirements, interval pattern recognition algorithms and the accompanying auxiliary computational procedures have been developed. These algorithms were designed for specific samples provided by the users (short samples, the presence of rare events in them or difficulties in the construction of interpretation scenarios). They have the common property that the original optimization procedures are built for them or well-known optimization procedures are used. This paper presents a series of results on processing observations by allocating large outliers as in a time series in planar and spatial observations. The algorithms presented in this paper differ in speed and sufficient validity in terms of the specially selected indicators. The proposed algorithms were previously tested on specific measurements and were accompanied by meaningful interpretations. According to the author, this paper is more applied than theoretical. However, to work with the proposed material, it is required to use a more diverse mathematical tool kit than the one that is traditionally used in the listed applications. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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17 pages, 460 KiB  
Article
The Geo/Ga,Y/1/N Queue Revisited
by Mohan Chaudhry and Veena Goswami
Mathematics 2022, 10(17), 3142; https://doi.org/10.3390/math10173142 - 01 Sep 2022
Cited by 2 | Viewed by 840
Abstract
We not only present an alternative and simpler approach to find steady-state distributions of the number of jobs for the finite-space queueing model Geo/Ga,Y/1/N using roots of the inherent characteristic equation, but [...] Read more.
We not only present an alternative and simpler approach to find steady-state distributions of the number of jobs for the finite-space queueing model Geo/Ga,Y/1/N using roots of the inherent characteristic equation, but also correct errors in some published papers. The server has a random service capacity Y, and it processes the jobs only when the number of jobs in the system is at least ‘a’, a threshold value. The main advantage of this alternative process is that it gives a unified approach in dealing with both finite- and infinite-buffer systems. The queue-length distribution is obtained both at departure and random epochs. We derive the relation between the discrete-time Geo/Ga,Y/1/N queue and its continuous-time analogue. Finally, we deal with performance measures and numerical results. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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17 pages, 2164 KiB  
Article
Really Ageing Systems Undergoing a Discrete Maintenance Optimization
by Radim Briš and Pavel Jahoda
Mathematics 2022, 10(16), 2865; https://doi.org/10.3390/math10162865 - 11 Aug 2022
Cited by 2 | Viewed by 1037
Abstract
In general, a complex system is composed of different components that are usually subject to a maintenance policy. We take into account systems containing components that are under both preventive and corrective maintenance. Preventive maintenance is considered as a failure-based preventive maintenance model, [...] Read more.
In general, a complex system is composed of different components that are usually subject to a maintenance policy. We take into account systems containing components that are under both preventive and corrective maintenance. Preventive maintenance is considered as a failure-based preventive maintenance model, where full renewal is realized after the occurrence of every nth failure. It offers an imperfect corrective maintenance model, where each repair deteriorates the component or system lifetime, the probability distribution of which gradually changes via increasing failure rates. The reliability mathematics for unavailability quantification is demonstrated in the paper. The renewal process model, involving failure-based preventive maintenance, arises from the new corresponding renewal cycle, which is designated a real ageing process. Imperfect corrective maintenance results in an unwanted rise in the unavailability function, which can be rectified by a properly selected failure-based preventive maintenance policy; i.e., replacement of a properly selected component respecting both cost and unavailability after the occurrence of the nth failure. The number n is considered a decision variable, whereas cost is an objective function in the optimization process. The paper describes a new method for finding an optimal failure-based preventive maintenance policy for a system respecting a given reliability constraint. The decision variable n is optimally selected for each component from a set of possible realistic maintenance modes. We focus on the discrete maintenance model, where each component is realized in one or several maintenance mode(s). The fixed value of the decision variable determines a single maintenance mode, as well as the cost of the mode. The optimization process for a system is demanding in terms of computing time because, if the system contains k components, all having three maintenance modes, we need to evaluate 3k maintenance configurations. The discrete maintenance optimization is shown with two systems adopted from the literature. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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0 pages, 1879 KiB  
Article
Deep Machine Learning Model-Based Cyber-Attacks Detection in Smart Power Systems
by Abdulaziz Almalaq, Saleh Albadran and Mohamed A. Mohamed
Mathematics 2022, 10(15), 2574; https://doi.org/10.3390/math10152574 - 25 Jul 2022
Cited by 18 | Viewed by 3096 | Correction
Abstract
In this study, a deep learning-based attack detection model is proposed to address the problem of system disturbances in energy systems caused by natural events like storms and tornadoes or human-made events such as cyber-attacks. The proposed model is trained using the long [...] Read more.
In this study, a deep learning-based attack detection model is proposed to address the problem of system disturbances in energy systems caused by natural events like storms and tornadoes or human-made events such as cyber-attacks. The proposed model is trained using the long time recorded data through accurate phasor measurement units (PMUs). The data is then sent to various machine learning methods based on the effective features extracted out using advanced principal component analysis (PCA) model. The performance of the proposed model is examined and compared with some other benchmarks using various indices such as confusion matrix. The results show that incorporating PCA as the feature selection model could effectively decrease feature redundancy and learning time while minimizing data information loss. Furthermore, the proposed model investigates the potential of deep learning-based and Decision Tree (DT) classifiers to detect cyber-attacks for improving the security and efficiency of modern intelligent energy grids. By utilizing the big data recorded by PMUs and identifying relevant properties or characteristics using PCA, the proposed deep model can effectively detect attacks or disturbances in the system, allowing operators to take appropriate action and prevent any further damage. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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14 pages, 544 KiB  
Article
Theoretical Bounds on the Number of Tests in Noisy Threshold Group Testing Frameworks
by Jin-Taek Seong
Mathematics 2022, 10(14), 2508; https://doi.org/10.3390/math10142508 - 19 Jul 2022
Cited by 2 | Viewed by 884
Abstract
We consider a variant of group testing (GT) models called noisy threshold group testing (NTGT), in which when there is more than one defective sample in a pool, its test result is positive. We deal with a variant model of GT where, as [...] Read more.
We consider a variant of group testing (GT) models called noisy threshold group testing (NTGT), in which when there is more than one defective sample in a pool, its test result is positive. We deal with a variant model of GT where, as in the diagnosis of COVID-19 infection, if the virus concentration does not reach a threshold, not only do false positives and false negatives occur, but also unexpected measurement noise can reverse a correct result over the threshold to become incorrect. We aim to determine how many tests are needed to reconstruct a small set of defective samples in this kind of NTGT problem. To this end, we find the necessary and sufficient conditions for the number of tests required in order to reconstruct all defective samples. First, Fano’s inequality was used to derive a lower bound on the number of tests needed to meet the necessary condition. Second, an upper bound was found using a MAP decoding method that leads to giving the sufficient condition for reconstructing defective samples in the NTGT problem. As a result, we show that the necessary and sufficient conditions for the successful reconstruction of defective samples in NTGT coincide with each other. In addition, we show a trade-off between the defective rate of the samples and the density of the group matrix which is then used to construct an optimal NTGT framework. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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16 pages, 304 KiB  
Article
Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time
by P. -C. G. Vassiliou
Mathematics 2022, 10(8), 1214; https://doi.org/10.3390/math10081214 - 07 Apr 2022
Cited by 2 | Viewed by 1610
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
25 pages, 2412 KiB  
Article
Introducing a Novel Method for Smart Expansive Systems’ Operation Risk Synthesis
by Nikolay Zhigirev, Alexander Bochkov, Nataliya Kuzmina and Alexandra Ridley
Mathematics 2022, 10(3), 427; https://doi.org/10.3390/math10030427 - 28 Jan 2022
Cited by 4 | Viewed by 1580
Abstract
In different areas of human activity, the need to choose optimal (rational) options for actions from the proposed alternatives inevitably arises. In the case of retrospective statistical data, risk analysis is a convenient tool for solving the problem of choice. However, when planning [...] Read more.
In different areas of human activity, the need to choose optimal (rational) options for actions from the proposed alternatives inevitably arises. In the case of retrospective statistical data, risk analysis is a convenient tool for solving the problem of choice. However, when planning the growth and development of complex systems, a new approach to decision-making is needed. This article discusses the concept of risk synthesis when comparing alternative options for the development of a special class of complex systems, called smart expansive systems, by the authors. “Smart” in this case implies a system capable of ensuring a balance between its growth and development, considering possible external and internal risks and limitations. Smart expansive systems are considered in a quasi-linear approximation and in stationary conditions of problem-solving. In general, when the alternative to comparison is not the object itself, but some scalar way of determining risks, the task of selecting the objects most at risk is reduced to assessing the weights of factors affecting the integral risk. As a result, there is a complex task of analyzing the risks of objects, solved through the amount by which the integral risk can be minimized. Risks are considered as anti-potentials of the system development, being retarders of the reproduction rate of the system. The authors give a brief description of a smart expansive system and propose approaches to modeling the type of functional dependence of the integral risk of functioning of such a system on many risks, measured, as a rule, in synthetic scales of pairwise comparisons. The solution to the problem of reducing the dimension of influencing factors (private risks) using the vector compression method (in group and inter-scale formulations) is described. This article presents an original method for processing matrices of incomplete pairwise comparisons with indistinctly specified information, based on the idea of constructing reference-consistent solutions. Examples are provided of how the vector compression method can be applied to solve practical problems. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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10 pages, 310 KiB  
Article
New Applied Problems in the Theory of Acyclic Digraphs
by Gurami Tsitsiashvili and Victor Bulgakov
Mathematics 2022, 10(1), 45; https://doi.org/10.3390/math10010045 - 23 Dec 2021
Cited by 1 | Viewed by 1903
Abstract
The following two optimization problems on acyclic digraph analysis are solved. The first of them consists of determining the minimum (in terms of volume) set of arcs, the removal of which from an acyclic digraph breaks all paths passing through a subset of [...] Read more.
The following two optimization problems on acyclic digraph analysis are solved. The first of them consists of determining the minimum (in terms of volume) set of arcs, the removal of which from an acyclic digraph breaks all paths passing through a subset of its vertices. The second problem is to determine the smallest set of arcs, the introduction of which into an acyclic digraph turns it into a strongly connected one. The first problem was solved by reduction to the problem of the maximum flow and the minimum section. The second challenge was solved by calculating the minimum number of input arcs and determining the smallest set of input arcs in terms of the minimum arc coverage of an acyclic digraph. The solution of these problems extends to an arbitrary digraph by isolating the components of cyclic equivalence in it and the arcs between them. Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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Other

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11 pages, 1160 KiB  
Correction
Correction: Almalaq et al. Deep Machine Learning Model-Based Cyber-Attacks Detection in Smart Power Systems. Mathematics 2022, 10, 2574
by Abdulaziz Almalaq, Saleh Albadran and Mohamed A. Mohamed
Mathematics 2024, 12(7), 934; https://doi.org/10.3390/math12070934 - 22 Mar 2024
Viewed by 345
Abstract
The authors wish to make the following corrections to this paper [...] Full article
(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks)
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