About insensibility of stationary distribution of state probabilities of open queueing network with multimode strategies and polytypic demands

The open queuing network with demands of M types is considered in article. The incomingflow is Poisson with intensity ƒ. The single line units can work in some strategies. Every strategyresponds to different degree of serviceability. The dispatching rule of demands by device of l unitis LCFS FS PR (l =1,N ) . Servicing time is random variable with arbitrary distribution function.The network state at the time t is characterized by vector x(t) = (x1(t), x2(t), …,xN(t)), wherestate of l unit at the time t is described by vector xl(t) = (xl(t), jl(t)) = (xl1(t), xl2(t), …, xl,n(l)(t),jl(t)), xl1(t) is the type of demand, which stands on the final position in l unit at the time t, xl,n(l)(t)is the type of demand, which is servicing by device in l unit at the time t, n(l) is total amount ofdemands in l unit, jl(t) is the number of device strategy in l unit at the time t, l =1,N .The durations of demands' service in units are mutually independent, don't depend on the arrivingprocess and on durations of staying devices in strategies and have arbitrary distributionfunction Bl(xl,u

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