Abstract. An algorithmic approach to study the queuing models with common finite and infinite buffer and jump priorities is developed. It is assumed that upon arrival of a low-priority call, one call of such kind might be transferred to the end of the queue of high-priority calls. The transfer probability depends on the state of the queue of heterogeneous calls. The algorithms are proposed to calculate the quality of service metrics of such queuing models.

Keywords: queuing system, priority jump, phase integration of states of Markov chains, numerical analysis.