The multi-server queueing system with a finite of an infinite buffer, with semi-Markovian input
flow (for positive and negative customers) and with Markovian Service Process (for positive
customers) whose the number of the states of the process and the intensities of the transitions
between phases depend on the number of the customers in the system is considered. An arriving
negative customer kills the one positive customer at the end of the queue. The relations and
algorithms for computation of the steady-state probabilities and for calculation of the steadystate
distribution of waiting time of positive customer are received. It is shown how the multiserver
queueing system with semi-Markovian input flow, the servicing of the phase type and
the above mentioned order of act of the negative customers can be bring to the general queuing
system
