The M|M|∞ queue transient probabilities

Abstract

In the theory and applications of queuing systems, transient probabilities play a key role. Often, due to the difficulty of their calculation they are replaced by the stationary probabilities. In the case of M|G|∞ systems, those calculations are much friendlier than usual. We present in this work formulas for the transient probabilities of the M|M|∞ system, where are considered service times with exponential distribution, showing that it is also possible to calculate them with initial conditions different from those usually considered.