The busy period distribution of the superposition of periodic arrivals with vacation time

This paper considers the output process resulting from aggregating M sources, each aggregate of which comprises a superposition of Ni identical constant bit-rate flows. For this output process we give a closed-form expression of the busy period distribution, when the first packet of the busy period encounters a delay, called the vacation. This expression is compared to simulation results for the busy period and waiting time. The theoretical and experimental distributions match closely.