Analysis in non-stationary regime of exponential G-network with bypass of queueing systems positive customers

The study of an open exponential queuing network (SEMO) with single-line queuing systems (QS) is carried out. QS are characterized by the presence of bypasses, positive orders and the possibility of receiving negative orders in them. The network receives two independent simplest flows of applications. The first flow is formed from ordinary (positive) customers, the second - from negative customers, the arrival of each of which into the system destroys exactly one positive customer in the queue, if any. Negative orders do not require service; positive orders are serviced in the network systems in accordance with the FIFO discipline. Positive claims with a probability depending on the state of the node when they are directed to it join the queue, and with an additional probability they instantly bypass it and behave in the future as served. To solve the system of difference-differential equations (RDE) for non-stationary probabilities of states of a network operating in saturation mode, it is proposed to use the method of multidimensional generating functions.

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