Computer-controlled queuing system with general access-cycle times

The paper presents a detailed study of a computer-controlled queuing system with Poisson input, first-come first served queue discipline, multiple exponential severs and general access-cycle times. A generating function for the state probabilities of, and the necessary and sufficient condition for the existence of, statistical equilibrium for the system are obtained. Further, the average number of customers in the system is derived from the generating function.