The paper deals with the queueing system for customers with Poisson’s input current intensity l and two service modes: in the regular service regime of intensity control m, customers are served with probability p»1 and in the special regime of servicing the special customers with intensity x. The special customers access the REQS with complementary probability (1-p)»0. The special customer service is analogous to a rare event. The standard methodology has developed analytical patterns for the stationary of REQS with one service channel and an infinite number of positions in the queue. The analysis of the work of REQS indicates that it is for favorable metering parameters r=l/m>2, queueing system is resistant to collapse when a occurrence occurs. However, the regular time losses of the regular customers in the REQS are extremely high. For this reason, it is the first time that the period of stabilization of the system is promoted which represents the time interval service the completion of the special customers until the REQS. The analytical apparatus of the queueing system has shown excellent adaptability to the heterogeneous demands of services m and special customers with low service intensity x, where m>x. The system can be applied to checkpoint calculations, the traffic cuts due to accidents, incidents to industrial systems, ie, the rare events due to anthropogenic and technical factors in intervals of 10^-4 do 10^-6. The model is not intended for natural hazards.