Computer-controlled queuing system with switching network and blocked customers are loss

The paper presents a detailed study of a computer-controlled queuing system with Poisson input, first-come first served queue discipline, multiple exponential servers, switching network and blocked customers leave the system permanently without services. 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 employment of the theory of Markov chains.