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1 Journal of Applied Mathematics and Computational Mechanics

1 2020

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Investigation of G-network with bypasses of queueing systems by positive customers at a non-stationary regime

Naumenko Victor, Kopats Dmitry, Matalytski Mikhail, Pankov Andrey

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 3

85--97

An open queuing network (QN) with single-line queuing systems (QS) is considered. QS are characterized by the presence of bypasses and the possibility of coming of negative customers. The network receives two independent elementary streams. The first stream is formed from the ordinary (positive) customers, while the second is composed of negative customers. Arriving of each negative customer to the system destroys exactly one positive customer in the queue, if those are contained. Negative customers do not require maintenance as the service of positive customers in the network systems is carried out in accordance with the FIFO discipline. Positive customers with a probability depending on the state of the node when they are sent to it are added to the queue, and with an additional probability, they immediately bypass it and behave in the future as served. The service in the systems is exponential, the routing of positive customers in the network is Markov, taking into account the possibility of turning the customer into a negative one after sending it to another system.