Asymptotic analysis of a closed G-network with rewards - Rusilko, Tatiana V. (Вестник Томского государственного университета. Управление, вычислительная техника и информатика)
A closed exponential G-network with positive and negative customers is studied. In addition, the G-network under study generates a sequence of rewards or earnings associated with network transitions from one state to another. The total network reward is a random process governed by the probabilistic relations of the Markov process that determines the number of customers in the network nodes. The purpose of this paper is to asymptotically study the G-network with rewards under the assumption of a large number of customers. The main objective is to calculate the expected total reward of the G-network in the asymptotic case. It is proved that reward density function satisfies the generalized Kolmogorov back-ward equation. An ordinary differential equation for the expected reward that the G-network will earn in a time t if it starts in a given initial state, is derived.