Insensibility of stationary distribution of queueing network with multimode strategies states when parameters of the servicing and switching processes are dependent on unit state

The open queueing network with polytypic demands is considered in the article. The single line units can work in some strategies. The quantity of the work which are necessary for servicing of demand and for switching from one strategy to another are random variables with arbitrary distribution function. The parameters of servicing and switching processes are dependent on the general unit state. It was proved that stationary distribution is invariant in relation to functional form of distribution of work’s quantities which are necessary for servicing of demands and switching of strategies, on condition that first moments are fast.