A note on the sojourn time distribution of an M/G/1 queue with a single working vacation and vacation interruption

We study the paper of Gao and Liu (2013). In the paper, the authors pay little attention to the customer’s sojourn time in their model although both the queue length and the busy cycle are seriously analyzed. The objective of this note is to derive the sojourn time distribution of Gao and Liu’s model without considering Bernoulli schedule. A simple numerical example is also given to demonstrate our result.