On finite capacity queueing systems with a general vacation policy (Q5932233)

For an M/G/1 queue with finite capacity and a general vacation policy, the author in an earlier paper [Queueing Syst. 3, No. 1, 41-52 (1988; Zbl 0655.60091)] derived the stationary queue length distributions immediately after a departure and at an arbitrary epoch. In the present note, using the previous results a relation between the two distributions, which extends a result given by \textit{A. Frey} and \textit{Y. Takahashi} [Oper. Res. Lett. 21, No. 2, 95-100 (1997; Zbl 0893.90065)], is obtained.