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“Informatics and Applications” scientific journalVolume 11, Issue 4, 2017Content Abstract and Keywords About Authors METHOD OF MODELING INTERFERENCE CHARACTERISTICS IN HETEROGENEOUS FIFTH GENERATION WIRELESS NETWORKS WITH DEVICE-TO-DEVICE COMMUNICATIONS
Abstract: The paper shows the construction of the model of the moving of interacting devices in heterogeneous wireless networks of the fifth generation with the help of the kinetic equation taking into account a given average speed of the devices, their spatial density, and the maximum allowable communication radius. A method for generating trajectories is proposed where the transceivers move randomly and the walk is not stationary in general.
Keywords: wireless heterogeneous network; signal-interference ratio; device-to-device (D2D); motion model; kinetic equation; trajectories generation; network efficiency indicators M/G/1 QUEUE WITH STATE-DEPENDENT HETEROGENEOUS BATCH ARRIVALS, INVERSE SERVICE
Abstract: Consideration is given to the stationary characteristics of single-server queues with the queue of infinite capacity, independent and identically-distributed service times, LCFS (last-come-first-served) service order, and probabilistic priority discipline. Most of the results for such type of queueing systems have been obtained under the assumption of either Poisson arrivals or phase-type arrivals. Another important assumption made was that the arrival process is independent from the system state. The author shows that the latter assumption can be relaxed to some, quite large extent. The author considers an M/G/ 1/to queue with batch Poisson arrival flow in which (i) the arrival rate depends on the total number of customers present in the system at the arrival instant; and (ii) the size of the arriving batch k and the remaining service times x±,..., xk of the customers in the batch have the arbitrary continuous joint probability distribution Bk(x i,..., xk). The author obtains analytic expressions for the computation of the joint stationary distribution of the total number of customers in the system and their remaining service times. Busy period, waiting and sojourn time distributions are also given in terms of the Laplace-Stieltjes transforms. Keywords: queueing system; LIFO; probabilistic priority; batch arrival; state-dependent Poisson flow STATIONARY SOJOURN TIMES IN MAP/PH/1 /r QUEUE WITH BI-LEVEL HYSTERETIC CONTROL OF ARRIVALS
Abstract: This paper reports some new results concerning the analysis of the time-related stationary characteristics of a finite-capacity queueing system operating in a random environment with the bi-level hysteretic control of arrivals. The topic of the paper is motivated by the overload problem in networks of SIP (session initiation protocol) servers and the viewpoint that multilevel hysteretic control of arrivals in SIP servers can be used to mitigate signalling network congestion. The considered mathematical model of SIP server is the single server queueing system with Markovian arrival processes (MAP), PH (phase-type) service, and bi-level hysteretic control policy According to this policy, a system may be in one of the three operation modes: normal, overload, or blocking. The switching between modes occurs at instants whenever the total number of customers in the system changes. The analytical method for the computation of the stationary sojourn times in different operation modes (in terms of Laplace-Stieltjes transforms (LST)), which utilizes the knowledge about the presence of hysteretic loops, is given. It is also applicable in the case when, in addition to the sojourn times, one needs to account for the number of lost customers. Keywords: queueing system; random environment; first passage times; hysteretic control SOME PROPERTIES OF THE MITTAG-LEFFLER DISTRIBUTION AND RELATED PROCESSES
Abstract: The paper contains an overview of some properties of the Mittag-Leffler distribution. Main attention is paid to its representability as a mixed exponential law The possibility to represent the Mittag-Leffler distribution as a scale mixture of half-normal and uniform distributions is discussed as well. It is shown that the Mittag-Leffler distribution can be used as an asymptotic approximation to the distributions of several statistics constructed from samples with random sizes. A new two-stage grid method for the estimation of the parameter of the Mittag-Leffler distribution is described. This method is based on the representation of the Mittag-Leffler distribution as a mixed exponential law Two ways are considered to extend the notion of the Mittag-Leffler distribution to Poisson-type stochastic processes. The first way leads to a special mixed Poisson process and the second leads to a special renewal process simultaneously being a doubly stochastic Poisson process (Cox process). In limit theorems for randomly stopped random walks in both of these cases, the limit laws are fractionally stable distributions representable as normal scale mixtures with different mixing distributions. Keywords: Mittag-Leffler distribution; Linnik distribution; stable distribution; Weibull distribution; exponential distribution; mixed Poisson process; renewal process; asymptotic approximation PATTERN-BASED ANALYSIS OF PROBABILISTIC AND STATISTICAL CHARACTERISTICS OF EXTREME PRECIPITATION
Abstract: Precipitations are the key parameters of hydrological models; so, research related to precipitation processes is necessary for solving various applied problems. The paper demonstrates a violation of the Markov property for precipitation observed in essentially different climatic regions - in the cities of Potsdam and Elista.
Keywords: precipitations; patterns; forecast; neural networks; probabilistic forecasting; Markov property METHOD OF ANALYSIS OF FUNCTIONAL VULNERABILITY OF FLOW NETWORK SYSTEMS
Abstract: Mathematical methods of analysis of network systems for transfer of streams of interchangeable products to various users are considered. For description of processes occurring in the system, the model of single-product flow network is used. Changes of functional characteristics of a system after the targeted destroying effects are studied according to the methodology of an operations research. The method of obtaining guaranteed damage estimates for each of the equal users of the complete destruction of the physical and logical elements of the system is proposed. The estimates are based on the solution of the sequence of vector optimization problems with lexicographic minimax criterion. To determine the strategy of flow distribution, a posteriori information about changes of network's capacity is used. Keywords: single-product flow network; functional vulnerability; damage assessment; principle of the guaranteed result ABOUT THE PROBLEM OF PROFIT MAXIMIZATION IN G/M/1 QUEUING SYSTEMS WITH THRESHOLD CONTROL OF THE QUEUE
Abstract: The problem of maximizing the average profit per time in G/M/1 queuing systems is considered on the set of stationary access restriction threshold strategies with one "switch point." Profit is defined as the following measures: service fee; hardware maintenance fee; fine for service delay; fine for unhandled requests; and fine for system idle. The authors formulated the necessary and sufficient conditions for optimality of the finite threshold value. The authors developed a method of sequential descent to the optimal threshold. The authors proposed an algorithm for calculating the optimal threshold value and the corresponding value of the objective function. Keywords: queuing system; threshold strategy; optimization THE MODEL OF THE SET OF INFORMATION SPACES IN THE PROBLEM OF INSIDER DETECTION
Abstract: In the problem of insider detection, the approach to combining compromising data observed in different information spaces is developed. Accumulation of information in each space is considered as a random process. The considered approach is based on bans and semibans of probability measures in different information spaces. Boolean variables communicate with the help of sequences of events observed in the information spaces. Appearance of semibans corresponds to value " 1 " of the appropriate Boolean variables. Sequences of Boolean variables in different information spaces easily communicate by means of logical expressions. The expressions describe dangerous tendencies observed in different information spaces. Keywords: information security; insider; bans and semibans of probability measures; architecture of combining information sources ANALYSIS OF VERTICAL HANDOVER TIME IN HETEROGENEOUS WIRELESS NETWORKS
Abstract: In a heterogeneous wireless network, connectivity is simultaneously available using different radio networks with overlapping coverage areas. A mobile user equipment with a multiple mode card that can work under various frequency bands and modulation schemes can switch from one technology to another in order to maintain communication. This procedure known as a vertical handover (VHO) provides the benefit of utilizing the higher bandwidth and lower cost of wide local area networks as well as better mobility support and larger coverage of cellular networks. The authors investigate details of the VHO procedure from WLAN (Wireless Local Area Network) to the 3GPP Long Term Evolution (LTE). The VHO procedure includes 40 signaling messages, which are responsible for authorization and resource allocation in the target LTE network. The authors analyze the VHO sojourn time and its 95 percent quantile using a multiphase queuing system with background traffic. Keywords: heterogeneous wireless network; cellular network; LTE; mobility; session setup procedure; connection reliability; connection availability; performance measure PERFORMANCE MEASURES ANALYSIS OF DATA TRANSFER PROCESS TO MOBILE USERS IN LTE CELL
Abstract: The goal of the study is to analyze the average transmission time in multicasting heterogeneous wireless networks, considering user movements within a cell under the condition that the cell can be divided into several areas with different channel quality. This performance measure is analyzed against the volume oftransmitted data and number of users in a cell. Three different motion models describing user movements within a cell are studied. In order to find out the average transmission time, an approach based on Markov control processes was implemented. Keywords: multicasting; heterogeneous wireless network; quality of service; Markov control process; motion model; average transmission time; dual process; queuing network DEVELOPMENT OF THE MATHEMATICAL MODEL OF CARGO TRANSPORTATION CONTROL ON A RAILWAY NETWORK SEGMENT TAKING INTO ACCOUNT RANDOM FACTOR
Abstract: A mathematical model for the assignment of locomotives for the transport of freight trains is proposed.
Keywords: mathematical modeling; optimization; transportation planning; operational planning THE USE OF WAVELETS FOR THE CALCULATION OF LINEAR CONTROL SYSTEMS WITH LUMPED PARAMETERS
Abstract: In many disciplines, problems appear which can be formulated with the aid of differential or integral equations. In simpler cases, such equations can be solved analytically, but for more complicated cases, numerical procedures are needed. In recent times, the wavelet-based methods have gained great popularity, where different wavelet families such as Daubechies, Coiflet, etc. wavelets are applied. A shortcoming of these wavelets is that they do not have an analytic expression. For this reason, differentiation and integration of these wavelets are very complicated. The paper presents algorithms for the numerical solution of linear integral and differential equations based on spline wavelets on the interval. The algorithms generalize the well-known methods based on Haar wavelets, which are a particular case of spline wavelets. The results presented can be applied for the analysis of linear systems with lumped parameters. Keywords: spline wavelet; differential equation; integral equation GAMMA-EXPONENTIAL FUNCTION IN BAYESIAN QUEUEING MODELS
Abstract: This paper considers the Bayesian approach to queueing theory and reliability theory. The Bayesian approach is useful for studying systems with alternating characteristics, the changes in which happen at the moments of time unpredictable for a researcher, or large groups of systems of the same type. In the framework of this approach, it is assumed that key parameters of classical systems are not given and only their a priori distributions are known. By randomizing the system's parameters, the authors randomize its characteristics, for instance, the traffic intensity. The gamma-exponential function and some of its properties are introduced as well as the results for probability characteristics of the system's traffic intensity and the probability that the claim received by the system will not be lost in the cases of the exponential and Weibull a priori distributions of M/M/1/0 system's parameters. Keywords: Bayesian approach; queuing systems; reliability; mixed distribution; Weibull distribution; exponential distribution; gamma-exponential function STUDY OF THE MMPP/GI/w QUEUEING SYSTEM WITH RANDOM CUSTOMERS' CAPACITIES
Abstract: A queueing system with an infinite number of servers is considered. Customers arrive in the system according to a Markov Modulated Poisson Process (MMPP). Each customer carries a random quantity of work (capacity of the customer). In this study, service time does not depend on the customers' capacities; the latter are used just to fix some additional features of the system's evolution. It is shown that the joint probability distribution of the customers' number and total capacities in the system is two-dimensional Gaussian under the asymptotic condition of an infinitely growing service time. Simulation results allow determining the applicability area of the asymptotic result. Keywords: infinite-server queueing system; random capacity of customers; Markov Modulated Poisson Process APPROACHES TO ANNOTATION OF DISCOURSE RELATIONS IN LINGUISTIC CORPORA
Abstract: This paper examines the Supracorpora Database of Connectives (SCDB-Connectives) that is based on data from parallel corpora. The SCDB-Connectives provides structural and semantic annotation of Russian connectives and their translation correspondences in French (and, eventually, in other languages). The SCDB- Connectives annotation approach is compared to the latest developments in the area of annotation of discourse relations - the annotated corpus of discourse relations Penn Discourse Treebank (PDTB) and the proposed standard for annotation of semantic relations ISO 24617-8, some of the important differences are discussed. Penn Discourse Treebank and ISO 24617-8 allow annotating implicit discourse relations as well as explicit ones while SCDB-Connectives only annotates explicit relations, i. e., those expressed by connectives. Furthermore, PDTB and ISO 24617-8 provide a superior framework for annotating text spans for relation arguments, which allows annotating attribution for these arguments, such as source and type of the linked propositions. In addition, ISO 24617-8 specifies argument roles for asymmetrical discourse relations. On the other hand, the principle advantage of the SCDB-Connectives is that it allows annotating both connectives and their translation correspondences in parallel corpora, opening up new possibilities for contrastive studies. The SCDB-Connectives is based on a relational database rather than on the XML format, which helps to manage complex cross-linguistic data efficiently. Benefits of semantic annotation of connectives for both theoretical and practical purposes are also discussed. Keywords: discourse relations; discourse connectives; corpus linguistics; parallel corpora; supracorpora databases
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