The insensitivity of stationarynetwork states probability distribution for the networks with multi-regime servicestrategies, different types of the demands and LCFS PR service discipline.

The open queueing networks with multi-regime service strategies and with different types of demands are regarded in this paper. The enter input is Poisson. The single server which can workin finite number of regimes works in any node. Sojourn time in any regime depends on the nodestate and has the exponential distribution. Transition is able only on the neighbour regimes so thatthe server can change service regime as in empty state so in busy one. Regime can be tractate as workability indicator of the server. Zero state is regarded as majority state. The quantity of the work which necessary to carry out for demand service is continuous random variable with generaldistribution function and the finite expectation. Carry out rate of this work depends on the nodestate. The demands in the nodes are served in according to LCFS PR service discipline with remainsof the service. It is proved for described network that stationary state probability distributionhas the product form and does`nt depend on the functional form of work quantity distributionwhich necessary for the service of the demands in the nodes, that is P(x) = p1(x1) p2 (x2 ) Ўї...Ўї pN (xN ), where pl(xl) is stationary probability state distribution of the isolated node which is located in fictive environment with Poisson enter input.

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