Waiting-time distribution in computer-controlled queuing system

The paper presents two formulas for the determination of the waiting-time distribution in a computer-controlled queuing system with Poisson input, multiple-exponential servers and first-come-first-served queue discipline. The formulas obtained are expressed in terms of the stationary-state probabilities of the computer-controlled queuing system. One of the formulas is derived by means of the formula of total proability and the other is derived by the use of the theory of Markov chains. It is shown that, by virtue of a limiting process, the first formula obtained in the paper yields the waiting-time distribution in the conventional queuing system without computer control. Furthermore, application of the two formulas for the determination of waiting-time distribution is illustrated by an example.