Computer-controlled queuing system with feedback and swap times

The paper presents a detailed investigation of a computer-controlled queuing system with Poisson input, multiple exponential servers, first-come first-served queue discipline, feedback and fixed finite swap times. The swap time is the time needed for the allocated server to acquire necessary information about the customer to be served and set up a necessary connection. A generating function for the stationary state probabilities of, and the 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.