For $M^θ$/$M$/$1$ and $M^θ$/$M$/$1$/$m$ queues with threshold switching of service modes at the start of the service of the next customer algorithm for determining the stationary distribution of the number of customers and stationary characteristics (average queue length, average time waiting, the variance of the queue length, probability o f service customers for the case of bounded queue) is proposed. In the case when the minimum number o f incoming customers in the group is comparable to the value o f threshold $h$, the stationary characteristics are found in an explicit form. The results are verified by simulation models constructed with the assistance of GPSS World.

[1] Anisimov V. Switching Processes in Queueing Models. - London: ISTE, 2008. - 352 p.

[2] Dudin A. Optimal multithreshold control for a BMAP/G/1 queue with N service modes / / Queueing Systems. - 1998. - 30, № 3-4. - P. 273-287.

[3] Zhernovy K.Yu.Research of the system $M^θ$/$M$/$1$/$m$ with service mode switching and threshold blocking of request flow // Information Processes. - 2010. - 10, № 2. - P. 159-180.

[4] Zhernovyi K.Y. General model of the system $M^θ$/$M$/$1$/$m$ with a threshold strategy of functioning // Scientific Bulletin of Chernivtsi University. Mathematics. - 2011. - 1, № 3. - P. 26-37.

[5] Ryzhikov Yu.I. About the task of two-speed service // Problems of information transfer. - 1978. - 14, issue 2. - P. 105-112.

[6] Dudin A.H., Medvedev G. A., Melenets Y.V.Practicum on the computer on the theory of mass service. - Minsk: Electronic book BSU, 2003. - 109 p.

[7] Boev V. D . Systems Modeling. Instrumental means of GPSS World. - St. Petersburg: BHV-Peterburg, 2004. - 368 p.

[8] Zhernovyi Y. V. Simulation modeling of queuing systems. - Lviv: Publishing center of Ivan Franko National University of Lviv, 2007. - 312p.