Balking and reneging in M/G/1 systems with post-ponable interruptions

Summary This paper considers the effect of postponable interruptions on aM/G/1 queueing process where customers balk with probabilityn/N (n=0, 1, 2, …,N) and renege after having waited for a random length of time. The busy period process in which transitions from any state (m, n) to any other state are permitted without an intermediate passage to the empty state, is investigated employing the supplementary variable method and discrete transforms. Later, the general process in which busy periods alternate with idle periods has been discussed in terms of the busy period process and renewal distributions and finally the ergodic properties of the general process studied by appealing to some results of renewal theory.