The busy period of the migi1 vacation model with a bernoulli schedule

The server busy period for the M|G|1 vacation model with a Bernoulli schedule is studied. Simple expressions are found for (i) the conditional joint distribution of the busy period and number in the system at the end of a busy period given the number in the system at the beginning of the busy period, (ii) the ergodic distribution of the number in the system at a busy period initiation epoch, and (iii) the distribution of the depletion time at service initiation epochs. Expressions in the real domain for the key ingredients of die busy period are also given.