Studying the queue length in a single-server queuing system with unreliable server

The unreliable queuing system was studied in both the nonstationary and stationary modes. It was assumed that a Poisson flow of customers arrives to the system; the times of customer servicing and restoration of the server (servicing system) are random variables with arbitrary distributions; the flow of stable failures makes up the restoration process; the interfailure intervals are distributed hyperexponentially; and the waiting and sojourn times as well as the queue length are not limited.