Invariance of the Stationary Distribution of Networks with Bypasses and “Negative” Customers

Abstract

Consideration was given to the open networks of single-server nodes of two types. The nodes of the first type are characterized by bypasses, those of the second type, by the possibility of arrival of “negative” customers. Servicing of the “positive” customers is done in the nodes according to the FCFS discipline. “Positive” and “negative” customers make up simplest flows. Invariance of the stationary distribution of network states to the functional form of the distributions of times of customer servicing in the nodes of first type under fixed first moments of these distributions was established.