Wyniki wyszukiwania - BazTech

1

Asymptotic analysis of a closed G-network of unreliable nodes

Rusilko Tatiana

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

91--102

EN

A closed exponential queueing G-network of unreliable multi-server nodes was studied under the asymptotic assumption of a large number of customers. The process of changing the number of functional servers in network nodes was considered as the birth-death process. The process of changing the number of customers at the nodes was considered as a continuous-state Markov process. It was proved that its probability density function satisfies the Fokker-Planck-Kolmogorov equation. The system of differential equations for the first-order and second-order moments of this process was derived. This allows us to predict the expectation, the variance and the pairwise correlation of the number of customers in the G-network nodes both in the transient and steady state.

2

Investigation of G-networks with restart at a non-stationary mode and their application

Matalytski Mikhail, Naumenko Victor, Kopats Dmitry

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 2

41--51

EN

This article discusses the question of restarting the script, when restart is used by many users of the information network, which can be modelled as a G-network. Negative claims simulate the crash of the script and the re-sending of the request. Investigation of an open queuing network (QN) with several types of positive customers with the phase type of distribution of their service time and one type of negative customers have been carried out. Negative customers are signals whose effect is to restart one customers in a queue. A technique is proposed for finding the probability of states. It is based on the use of a modified method of successive approximations, combined with the method of a series. The successive approximations converge with time to a stationary distribution of state probabilities, the form of which is indicated in the article, and the sequence of approximations converges to the solution of the difference-differential equations (DDE) system. The uniqueness of this solution is proved. Any successive approximation is representable in the form of a convergent power series with an infinite radius of convergence, the coefficients of which satisfy recurrence relations, which is convenient for computer calculations. A model example illustrating the finding of time-dependent probabilities of network states using the proposed technique is also presented.

3

Expected volumes of requests in systems of the queueing network with a limited number of waiting places

Zając P., Matalytski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2017

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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.

4

Diffusion approximation of the network with limited number of same type customers and time dependent service parameters

Matalytski M., Kopats D.

Journal of Applied Mathematics and Computational Mechanics

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2016

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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.

5

Vehicular flow simulators based on complex queuing systems

Pasini L., Feliziani S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2013

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Vol. 17, No 3-4

155--180

EN

The crux of this paper is to demonstrate how it is possible to model systems of vehicular trafic by means of complex queuing network models. The objects comprising the library that we define in this work all follow the approach whereby they are composed of one or more queuing networks of service systems that are traversed by customers (vehicles).

6

Asymptotic analysis of the closed queueing structure with time-dependent service parameters and single-type messages

Matalytski M., Rusilko T., Pankov A.

Journal of Applied Mathematics and Computational Mechanics

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2013

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Vol. 12, nr 2

73--80

EN

A closed queueing structure is considered in the paper; the number of single-type messages is not constant and depends on time. The route of messages is given by an arbitrary stochastic matrix of transition probabilities. An asymptotic analysis of this structure in case of large number of service requests is conducted. The service parameters of each queueing system of this structure, as well as the probability of messages transition between systems, depend on time. A system of ordinary differential equations to calculate the average relative number of messages in each queueing system, depending on the time, was obtained.

7

The network probability model of one-type customer requests processing in an insurance company

Matalytski M., Rusilko T.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2012

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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.

8

Time-dependent state probabilities of queueing network with unreliable systems in transient regime

Matalytski M., Statkevich S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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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.

9

Optymalizacja sieci kolejkowych przy użyciu algorytmów genetycznych

Filipowicz B., Kwiecień J.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2003

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T. 7, z. 1-2

89-96

PL

W niniejszej pracy przedstawiono optymalizację otwartych sieci wykładniczych BCMP składających się z systemów kolejkowych M/M/m/FIFO/∞ za pomocą algorytmów genetycznych. W pracy scharakteryzowano sieć kolejkową BCMP. Podano krótką charakterystykę algorytmów genetycznych. Sformułowano zadanie optymalizacji sieci kolejkowej polegające na znalezieniu minimum funkcji celu przedstawiającej koszt eksploatacji sieci. Podczas optymalizacji poszukiwana była taka liczba kanałów obsługi w poszczególnych systemach, dla których koszty pracy sieci były najmniejsze. Przedstawiono wyniki optymalizacji dla sieci składającej się z czterech stacji i dwóch klas zgłoszeń.

EN

The application of genetic algorithms for optimization of open BCMP queueing network with M/M/m/FIFO/∞ systems was analysed in this paper. BCMP queueing network and genetic algorithm are briefly characterized. Optimization problem of queueing network with finding of minimum of target function representing the total operating cost of network, is formulated. The optimal number of servers (in all systems) for which operating costs are minimum are attained during optimization. Optimization example for queueing network which consists of four systems and two job classes is presented.