The busy period and the busy cycle probability study are critical in queue real-world practical applications. However, it is a challenging task. In this chapter, we show how to obtain a collection of service length distribution functions by solving a Riccati equation induced by this queue transient probabilities monotony study as time functions, for which both the busy period and the busy cycle have lengths with quite simple distributions, generally given in terms of exponential distributions and the degenerate at the origin distribution.
Manuel Alberto M. Ferreira
ISTAR-IUL – Information Sciences, Technologies and Architecture Research Center (ISTA), ISCTE-IUL – Instituto Universitário de Lisboa, Lisboa, Portugal.