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2 Journal of Applied Mathematics and Computational Mechanics

2 2013

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Nonstationary analysis of the queueing network with bypass of systems of multi-type and absolute priority messages

Matalytski M., Naumenko V.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 1

93--105

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.

Nonstationary analysis of a queueing network with positive and negative messages

Matalytski M., Naumenko V.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 2

61--71

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.