Asymptotic analysis of expected revenues in G-network with unreliable lines service and limited waiting time positive and negative customers

Abstract

We study G-network consisting of multiline unreliable queuing systems (QS) that receive impatient positive and negative requests and previously obtained results on asymptotic analysis and research of similar networks. The impatience of negative requests is manifested in the destruction of positive requests by them not immediately, but after a random time, and the impatience of positive ones is manifested in limiting the waiting time for the start of servicing positive requests, after which it can move along the network systems or leave the network. Using asymptotic analysis for a large but limited number of requests operating in the network, expressions for the expected income of this network are found. A system of difference-differential equations is obtained, which are satisfied by the expected incomes of the network systems. Next, an equation in partial derivatives is obtained for the income distribution density and a return to the expression for expected incomes is carried out. In conclusion, the findings of the work are presented and the prospects for studying queuing networks (QSN) using this method are noted