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2 Journal of Applied Mathematics and Computational Mechanics

2 2013

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The asymptotic analysis of the income in closed HM-structure with priority messages

Matalytski M., Kiturko O.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 2

51--59

In the article the asymptotic analysis of closed exponential queueing HM-structure with priority messages is carried out with a large total number of messages, depending on time. The number of service lines in systems, the intensity of service messages in them, the probabilities of message transitions between systems also depends on time. It is proved that the density of the income distribution in the network systems in asymptotic satisfies differential equations in partial derivatives. This provided the inhomogeneous differential equation for the expected incomes system structure. An example of transport logistics shows how to solve such equations.

Finding of the expected income of the closed queueing structure and its application in transport logistics

Matalytski M., Kiturko O.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 1

85--92

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).