Tandem service system with batch Markov flow and repeated calls

Consideration was given to the tandem queuing system (QS) whose first stage consists of a single-server system with batch Markov arrivals and repeated calls and the second stage consists of a multi-server QS without buffer. In the case of no idle servers in the second stage, the customer serviced at the first stage either waits for server release and at that blocks the first-stage service or discharges the system being serviced incompletely. The stationary distribution of the probabilities of system states at the embedded and arbitrary time instants and the main characteristics of system performance were established. Numerical examples were presented.