A generalised approach is presented for the study of a computer-controlled queuing system with general input, ‘first-come-first-served’ queue discipline and multiple servers with feedback for either exponential servers or constant service times. Two generating functions for the state probabilities of the system corresponding to the two different types of service times are derived. Further, necessary and sufficient conditions for the existence of statistical equilibrium of the computer-controlled queuing system are obtained from the generating functions. The results obtained here generalise many results previously obtained by other workers.