POISSOIN ARRIVALS, EXPONENTIAL SERVICE TIME, AND INFINITE SERVERS QUEUE BUSY PERIOD AND BUSY CYCLE DISTRIBUTION FUNCTIONS BOUNDS - Alberto M. Ferreira, Manuel (Acta Scientiae et Intellectus, 2024)
The busy period length distribution function knowledge is important for any queue system, and for thequeue. But the mathematical expressions are in general very complicated, with a few exceptions, involving usually infinite sums and multiple convolutions. So, in this work are deduced some bounds for thesystem busy period length distribution function, meaning the second M exponential service time, which analytic expressions are simpler than the exact one. As a consequence, also some bounds for the system busy cycle length distribution function are presented.