Nonstationary analysis of a queueing network with positive and negative messages

• Autorzy: Matalytski M. , Naumenko V.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

information systems; telecommunications systems; information networks; telecommunications networks; virus; open G-network with negative messages; transient behavior; system of difference-differential equations; probability states; generating function

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 2
• Strony: 61--71
• Opis fizyczny: Bibliogr. 3 poz., rys.

Twórcy

autor

Matalytski M.

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

autor

Naumenko V.

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

Bibliografia

• [1] Bocharov P.P., Vishnevski V.M., G-networks: the development of the theory of multiplicative networks, Automatic. Telemekh. 2003, 5, 46-74 (in Russian).
• [2] Gelenbe E., Stability of product-form G-networks, Probab. Eng. and Inf. Sci. 1992, 6, 271-276.
• [3] Gelenbe E., Product form queueing networks with negative and positive customers, J. Appl. Prob. 1991, 28, 656-663.