Computer-controlled queuing system with service interruptions

The paper presents a detailed study of a computer-controlled queuing system with Poisson input, first-come-first-served queue discipline and multiple-exponential servers that are subject to breakdowns and repairs. A generating function for the 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 first waiting-time distribution in the system is obtained by the use of the theory of Markov chains.