Computing the characteristics of a queueing system with repeated units and twin connections

A queueing system, QS, is considered with repeated units and two-staged service in a server; if at the first stage the server receives another unit, both units leave the server and become repeated; of at the first stage the service has been completed, the unit arrives at the second stage and the server becomes inaccessaible for the arriving units. The case of group arrival of units is taken up the function of service duration distribution being arbitrary at the second stage. Necessary and sufficient conditions are obtained for existence of a stationary mode as are generatrices of stationary probabilities of QS states that are used in computing the system performance characteristics.