Queuing system with infinite buffer and stepwise inflow intensity

The queuing system with infinite buffer, single server, and exponential servicing was considered. A double stochastic Poisson flow whose intensity $\lambda(t)$ is a stepwise process with exponentially distributed constancy intervals arrives to it. It was assumed that the values of process $\lambda(t)$ to the left and right of the discontinuity point were independent. The nonstationary and stationary characteristics were determined using the method of generating functions. Existence and uniqueness of the stationary mode and stabilization of the nonstationary queuing system mode were proved. The results of numerical analysis and application of the considered queuing system were discussed.