Analysis of Markov HM-Queueing Networks with FIFO discipline at the transient regime and its application

In the paper Markov Queueing Networks (QN) are considered with the same types and different types of customers and incomes, FIFO discipline, which are probabilistic models of different Information Nets and Systems (INS). The incomes from the state transition of the network depend on servicing times of customers in the Queueing Systems (QS). The purpose of the research are design and development of methods and techniques of finding the probability-cost characteristics in such QN as effective analysis tools of INS. A closed Markov HM-network with the same types of customers has been investigated. Approximate expressions for the expected incomes of the QS were obtained. The method of finding the mean number of the customers was proposed. The analysis of an open HM-network with different types of customers and many-server queues has been carried out in the second part of the paper. Customers during the transition between QS can change its type. Approximate expressions for the expected incomes of the QS for each type of customer have been also obtained. A method for finding the mean number of servicing lines was described.