Computer-controlled queuing system with switching network and blocked customers rejoin end of queue

The paper presents a detailed study of a computer-controlled queuing system with Poisson input, firstcome first-served queue discipline, multiple exponential servers, switching network and blocked customers feedback to the end of the queue. A generating function for the stationary-state probabilities of the system and a necessary and sufficient condition for the existence of statistical equilibrium for the system are derived. Further, a formula for the determination of the waiting-time distribution in the system is obtained by the use of the theory of Markov chains.