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Analysis of open queueing networks using method of generating functions

Matalycki M., Gomanczuk S., Pankow A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2002

Vol. 1, nr 1

143--152

This paper provides the method of generating functions using for calculating the time-dependent state probabilities for open queuing networks in transient regime, when the network works in conditions of peak demand.

Analysis of stochastic models of computer systems and networks in transient behaviour

Matałycki M., Gomanczuk S.

Informatyka Teoretyczna i Stosowana

2002

R. 2, nr 2

9-20

This paper provides an approximate numerical method of calculating of the time-dependent state probabilities of Markovian queueing networks, which can be used as models of various kinds of computer systems and networks. We consider queueing networks with multi channel devices and multi-type messages. The specified method is based on successive approximations idea for the set of difference-differential Kolmogorov equations, the state probabilities satisfy, combined with numeric series analyzing methods. We examined the successive approximations features and, as an example, we applied ibis method for calculating the state probabilities for two types of queueing networks: priority-service discipline network and the network with limited waiting time in queues.