The busy period of an M/M/1 queue with balking and reneging

It has been shown by (R.O. Al-Seedy, A.A. El-Sherbiny, S.A. El-Shehawy, S.I. Ammar, Transient solution of the M/M/c queue with balking and reneging, Comput. Math. Appl. 57 (2009) 1280–1285) that a generating function technique can be successfully applied to derive the transient solution for an M/M/c queueing system. In this paper, we further illustrate how this technique can be used to obtain the busy period density function of an M/M/1 queue with balking and reneging. Finally, numerical calculations are presented.