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1
Content available Analysis of Markov HM-Queueing Networks with FIFO discipline at the transient regime and its application
100%
Matalytski M.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
tom Vol. 14, nr 3
65--77
EN
In the paper Markov Queueing Networks (QN) are considered with the same types and different types of customers and incomes, FIFO discipline, which are probabilistic models of different Information Nets and Systems (INS). The incomes from the state transition of the network depend on servicing times of customers in the Queueing Systems (QS). The purpose of the research are design and development of methods and techniques of finding the probability-cost characteristics in such QN as effective analysis tools of INS. A closed Markov HM-network with the same types of customers has been investigated. Approximate expressions for the expected incomes of the QS were obtained. The method of finding the mean number of the customers was proposed. The analysis of an open HM-network with different types of customers and many-server queues has been carried out in the second part of the paper. Customers during the transition between QS can change its type. Approximate expressions for the expected incomes of the QS for each type of customer have been also obtained. A method for finding the mean number of servicing lines was described.
2
Content available About one method of finding expected incomes in HM-queueing network with positive customers and signals
100%
Matalytski M.
Journal of Applied Mathematics and Computational Mechanics
|
2016
|
tom Vol. 15, nr 1
87--98
EN
In the paper an open Markov HM(Howard-Matalytski)-Queueing Network (QN) with incomes, positive customers and signals (G(Gelenbe)-QN with signals) is investigated. The case is researched, when incomes from the transitions between the states of the network are random variables (RV) with given mean values. In the main part of the paper a description is given of G-network with signals and incomes, all kinds of transition probabilities and incomes from the transitions between the states of the network. The method of finding expected incomes of the researched network was proposed, which is based on using of found approximate and exact expressions for the mean values of random incomes. The variances of incomes of queueing systems (QS) was also found. A calculation example, which illustrates the differences of expected incomes of HM-networks with negative customers and QN without them and also with signals, has been given. The practical significance of these results consist of that they can be used at forecasting incomes in computer systems and networks (CSN) taking into account virus penetration into it and also at load control in such networks.
3
Analiza asymptotyczna wykładniczej sieci kolejkowej z parametrami zależnymi od czasu
100%
Matalytski M.
Studia Informatica
|
2013
|
tom Vol. 34, nr 3
177--184
PL
W artykule przeanalizowano zamkniętą wykładniczą sieć kolejkową z dużą liczbą zgłoszeń i parametrami zależnymi od czasu. Otrzymano układ równań różnicowo-różniczkowych dla prawdopodobieństw stanów i układ równań różniczkowych do wyznaczenia średniej liczby zgłoszeń w systemach sieci. Obliczono przykład numeryczny
EN
The closed exponentional queueing network with the large number of messages and the time-dependent parameters is investigated. We have received the system of difference-differential equations for the state probabilities and system of differential equations for the average number of messages of network systems. The modeling example for their calculation is presented.
4
Content available remote Solution of optimal control problem for the three-level HM-network. Part 1
63%
Matalytski M. , Kiturko O.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2011
|
tom Vol. 10, nr 1
163-174
EN
We studied the three-level exponential HM queueing network with one type of requests and incomes, which is a stochastic model for goods transport in a logistics transport system. We obtained a system of difference equations for the expected income of the central system with and without a reduction of future income to the current time in the case of a finite and infinite control horizon maximizing the expected income of the central system. These problems are proposed to be solved by the method of complete enumeration control strategies.
5
Content available remote Time-dependent state probabilities of queueing network with unreliable systems in transient regime
63%
Matalytski M. , Statkevich S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2011
|
tom Vol. 10, nr 1
175-187
EN
The method of a multidimensional generating function for finding timedependent state probabilities of a open queuing network with unreliable systems is studied. Assuming that the network functions in the condition of heavy loading, the flow parameters of messages, servicing, duration of serviceable working and duration of restoration of channels are time-dependent. Such networks can serve as models of the functioning of the Local Area Network (LAN). Expressions for network state probabilities at any moment of time are obtained. An example for finding network state probabilities with a central system is considered.
6
Content available Application of a z-transforms method for investigation of Markov G-networks
63%
Matalytski M. , Naumenko V.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
tom Vol. 13, nr 1
61--73
EN
The purpose of this research paper is to find the expected incomes in open Markov queueing networks with incomes, positive and negative messages at any time by the multidimensional transformations. Investigations were carried out in cases when incomes from the network transitions between the states are deterministic functions not dependent on network states and time. It is assumed that all network systems are one-line. It was proved the theorem on the expression for the multidimensional z-transform. An algorithm was proposed for calculation of expected incomes. It is calculated an example on the PC.
7
Content available remote Analysis of networks with time-dependent transition probabilities and messages bypass between the queuing systems
63%
Matalytski M. , Naumenko V.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
|
tom Vol. 11, nr 4
93-104
EN
The object of investigation is an open exponential network with a messages bypass of systems in transient behavior. The purpose of the research is to find stationary probabilities of states and the average characteristics of the network when the transition probabilities between the messages and bypass systems of the network, parameters of the incoming flow of messages and services are time-dependent. To find the state probabilities and the characteristics of a network is used the apparatus for the multivariate generating functions. The examples are calculated on a computer.
8
Content available Expected volumes of requests in systems of the queueing network with a limited number of waiting places
63%
Zając P. , Matalytski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2017
|
tom Vol. 22
141--160
EN
We present a method of finding the expected volume of requests in HM-network with homogeneous requests and bypass of the queueing systems of requests. The case was considered when the volume changes associated with the transitions between the states of the network are deterministic functions, depending on the state of the network and time, and the systems are single line. It is assumed that the probability of the states of the network systems, the parameters of the entrance flow of the requests and the service depend on the time.
9
Content available remote The network probability model of one-type customer requests processing in an insurance company
63%
Matalytski M. , Rusilko T.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
|
tom Vol. 11, nr 1
73-83
EN
The subject of this paper is the stochastic model of client requests processed by an insurance company. The model takes into account the limited duration of insurance contracts and the dependence on time of requests service rate. A closed exponential queueing network with single-type messages is used as the model. The goal of the study is to solve the problem of finding the optimal number of employees of the insurance company on certain time intervals. The study is conducted in the asymptotic case of high network load. The results of this paper could be applied to optimize the functioning of insurance companies.
10
Content available remote Investigation of queueing network with unreliable systems and large number of messages
63%
Matalytski M. , Statkevich S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
|
tom Vol. 11, nr 1
85-97
EN
The Markov network with unreliable queueing systems and a large number of messages is investigated. The service channels of systems are exposed to random failure, besides the time of the proper functionality and the time of reconstruction of each channel of system has the exponential distribution with distinctive parameters. The system of difference-differential equations of Kolmogorov for the states probabilities is compiled. The partial differential equation for the probability density function of the vector of states is deduced. The systems of ordinary differential equations for an average number of messages and serviceable channels of network systems are received.
11
Content available Finding of the expected income of the closed queueing structure and its application in transport logistics
63%
Matalytski M. , Kiturko O.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
tom Vol. 12, nr 1
85--92
EN
Research of the closed exponential queueing structure with one-type messages and the income is conducted. The differential equation in partial derivatives for an income distribution density is received. The ordinary differential equation for its expected income is constructed at particular starting conditions. The offered method of its decision in a case when the intensity of the service of messages, the number of messages in networks, the number of lines of the service in systems, the matrix of probabilities of transitions of messages and the income from transitions between conditions of the closed queueing structure (CQS) depend on time is described. An example when change of parameters has seasonal nature is reviewed. Results of this article can be applied at the prediction of the income of the logistic transport system (LTS).
12
Content available Investigation of G-network with signals at transient behavior
63%
Matalytski M. , Naumenko V.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
tom Vol. 13, nr 1
75--86
EN
G-queueing network with positive messages and signals at transient behavior is considered. A system of difference-differential equations for the state probabilities of the network is obtained. To find them and the average characteristics of the network a technique was applied based on the use of apparatus of multivariate generating functions. An expression for the generating function was obtained. An example is calculated.
13
Content available remote Finding incomes of the HM-network with one-type messages bypass of systems
63%
Matalytski M. , Naumenko V.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
|
tom Vol. 11, nr 3
111-123
EN
The object of research is an open HM-network with one-type messages bypass of systems in the transient behavior. Two cases are considered: when incomes from transitions between network states are deterministic functions depending on states and time, and network systems are single-line, and when incomes from transitions between network states are functions depending on random variables. The purpose of the research is to find the expected incomes of such a network in both cases on condition that the probabilities of messages bypasses of systems network and the parameters of incoming flow of messages and services depend on time. Examples are considered.
14
Content available Analysis of the queueing network with a random bounded waiting time of positive and negative customers at a non-stationary regime
63%
Matalytski M. , Naumenko V.
Journal of Applied Mathematics and Computational Mechanics
|
2017
|
tom Vol. 16, nr 1
97--108
EN
In the first part of the article, an investigation of an open Markov queueing network with positive and negative customers (G-networks) has been carried out. The network receives two exponential arrivals of positive and negative customers. Negative customers do not receive service. The waiting time of customers of both types in each system is bounded by a random variable having an exponential distribution with different parameters. When the waiting time of a negative customer in the queue is over it reduces the number of positive customers per unit if the system has positive customers. The Kolmogorov system of difference-differential equations for non-stationary state probabilities has been derived. The method for finding state probabilities of an investigated network, based on the use of apparatus of multidimensional generating functions has been proposed. Expressions for finding the mean number of positive and negative customers in the network systems have also been found. In the second part the same network has been investigated, but with revenues. The case when revenues from the network transitions between states are random variables with given mean values has been considered. A method for finding expected revenues of the network systems has been proposed. Obtained results may be used for modeling of computer viruses in information systems and networks and also for forecasting of costs, considering the viruses penetration.
15
Content available Investigation of networks with positive and negative messages, many-lines queueing systems and incomes
63%
Naumenko V. , Matalytski M.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
tom Vol. 14, nr 1
79--90
EN
The analysis of an open Markov Queueing Network with positive and negative messages, many-lines queueing systems and incomes has been carried out. External arrivals to the network, service times of rates and probabilities of messages transition between queueing systems (QS) depend on time. A method for finding the expected incomes of the network systems, the expressions for the average number of messages at the systems has been proposed.
16
Finding of expected volumes of requests in systems of the queueing network with a limited amount of spaces of expectations
63%
Zając P. , Matalytski M.
Studia Informatica
|
2017
|
tom Vol. 38, nr 1B
89--104
EN
We present a method of finding the expected volume of requests in open HM-network with homogeneous requests, bypass of nodes the network service systems. Were considered a case where the changes in volumes associated with transitions between states of the network are deterministic functions dependent states of network and time, and service systems are single line. Assumed that the probability of state network systems, the parameters of entrance flow of messages and service depend on time.
PL
Opisano metodę znalezienia oczekiwanej objętości zgłoszeń w otwartej HM-sieci z jednorodnymi zgłoszeniami i obejściami węzłów sieci systemów obsługi. Rozpatrywano przypadek, gdy zmiany objętości związanych z przejściami między stanami sieci są deterministycznymi funkcjami, zależnymi od stanów sieci i czasu, a systemy obsługi są jednoliniowe. Zakłada się, że prawdopodobieństwo stanów systemów sieci, parametry strumienia wejściowego zgłoszeń i obsługi zależą od czasu.
17
Content available Nonstationary analysis of the queueing network with bypass of systems of multi-type and absolute priority messages
63%
Matalytski M. , Naumenko V.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
tom Vol. 12, nr 1
93--105
EN
This paper contains an investigation of an open exponential network with bypass of systems of multi-type messages with absolute priority in transient behavior. Messages with priority received by the node with the probability depending on the state system and the type of incoming messages are for service, forcing messages that are serviced or instant changes in the following system, and can leave the network. Network settings: the intensity of the incoming flow and the intensity of service of different types of messages in single-line systems and the conditional probabilities of transitions of messages between the systems are dependent on the time. We obtained a system difference-differential equations for the state probabilities of the network. To find the state probabilities of the network in the transitional behavior applied a methodology based on the use of the apparatus of multidimensional generating functions.
18
Content available Diffusion approximation of the network with limited number of same type customers and time dependent service parameters
63%
Matalytski M. , Kopats D.
Journal of Applied Mathematics and Computational Mechanics
|
2016
|
tom Vol. 15, nr 2
77--84
EN
The article presents research of an open queueing network (QN) with the same types of customers, in which the total number of customers is limited. Service parameters are dependent on time, and the route of customers is determined by an arbitrary stochastic transition probability matrix, which is also dependent on time. Service times of customers in each line of the system is exponentially distributed. Customers are selected on the service according to FIFO discipline. It is assumed that the number of customers in one of the systems is determined by the process of birth and death. It generates and destroys customers with certain service times of rates. The network state is described by the random vector, which is a Markov random process. The purpose of the research is an asymptotic analysis of its process with a big number of customers, obtaining a system of differential equations (DE) to find the mean relative number of customers in the network systems at any time. A specific model example was calculated using the computer. The results can be used for modelling processes of customer service in the insurance companies, banks, logistics companies and other organizations.
19
Content available remote Solution of optimal control problem for the three-level HM-network. Part 2
63%
Matalytski M. , Kiturko O.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2011
|
tom Vol. 10, nr 2
155-167
EN
A three-level HM queueing network with one type of requests and incomes, which is a stochastic model for goods transport in a logistics transport system is studied in this article. We studied the problems of control choice with and without a reduction of thecurrent time in the case of a finite and infinite control horizon maximizing the expected income of a central system. We have compared three methods to find optimal control: the method of complete enumeration strategies, Bellman's method of dynamic programming and Howard's method.
20
Content available Nonstationary analysis of a queueing network with positive and negative messages
63%
Matalytski M. , Naumenko V.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
tom Vol. 12, nr 2
61--71
EN
This paper contains an investigation of an open queueing network with positive and negative messages that can be used to model the behavior of viruses in information and telecommunication systems and networks. The purpose of research is investigation of such a network at the transient behavior. We consider the case when the intensity of the incoming flow of positive and negative messages and service intensity of messages do not depend on time. It is assumed that all queueing systems of network are one-line. We obtained a system difference-differential equations for the state probabilities of the network. To find the state probabilities of the network in the transitional behavior applied a methodology based on the use of the apparatus of multidimensional generating functions. We obtained an expression for generating function. An example is calculated.
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