Ergodicity and stability of a multi-phase service system with interlocks and an infinite queue at the input

A multi-phase service system with interlocks and an infinite queue of customers at the input is considered. For a given phase the service time of customers are independent and similarly distributed; they are also independent of the service time in other phases. A condition and an estimate are give of the rate at which the system reaches the stationary mode no mater what its initial state was. Also obtained are the condition for stability of stationary mode and an estimate of the degree to which the system characteristics deflect from stationary ones with small changes of service times in the phases.