Analysis of multi-server queueing system with semi-Markovian input flow and negative customers acted upon queue end

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