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

• Autorzy: Matalytski M. , Kopats D.

Identyfikatory

DOI

10.17512/jamcm.2016.2.10

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

queueing network; birth and death process; asymptotic analysis

PL

sieci kolejkowe; analiza asymptotyczna; proces losowy

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 2
• Strony: 77--84
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Matalytski M.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Kopats D.

• Faculty of Mathematics and Computer Science, Grodno State University Grodno, Belarus

Bibliografia

• [1] Kelly F.P., Williams R.J., Stochastic Networks. The IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York 1995.
• [2] Nykowska M., Model tandemowego systemu obsługi, Przegląd Statystyczny 1984, 29(3), 531--540.
• [3] Kobayashi H., Application of the diffusion approximation to queueing networks, Journal of ACM 1974, 21(2-3), 316-328, 456-469.
• [4] Gelenbe E., Probabilistic models of computer systems. Diffusion approximation waiting times and batch arrivals, Acta Informatica 1979, 12, 285-303.
• [5] Lebedev E.A., Chechelnitsky A.A., Diffusion approximation of queueing net with a semi-Markov input rate, Cybernetics 1991, 2, 100-103.
• [6] Medvedev G.A., On the optimization of the closed queuing system. Proceedings of the Academy of Sciences of the USSR, Technical Cybernetics 1975, 6, 65-73.
• [7] Medvedev G.A., Closed queuing systems and their optimization. Proceedings of the Academy of Sciences of the USSR, Technical Cybernetics 1978, 6, 199-203.
• [8] Rusilko T.V., The asymptotic analysis of closed queuing networks with time-dependent parameters and priority application, Vestnik of GrSU. Series 2, Mathematics. Physics. Computer Science, Computer Facilities and Management 2015, 2, 117-123.
• [9] Paraev Y.I., Introduction to Statistical Process Control Dynamics and Filtering, Soviet Radio, 1976.
• [10] Matalytski M.A., Rusilko T.V., Mathematical Analysis of Stochastic Models of Claims Processing in Insurance Companies, GRSU, Grodno 2007.
• [11] Rusilko T.V., Matalytski M.A. Queuing Network Models of Claims Processing in Insurance Companies, LAP LAMBERT Academic Publishing, Saarbrucken 2012.
• [12] Matalytski M.A., Kiturko O.M., Mathematical Analysis of HM-networks and its Application in Transport Logistics, GrSU, Grodno 2015.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.