We study the distributions of the overlap number and the overlapping time that a tagged customer experiences in a network of two infinite server queues in series. While allowing general service time distributions in both queues, we specify the results in some detail for the cases of exponential and deterministic service time distributions. We furthermore outline how one can obtain joint overlap number distributions in more general feedforward networks of infinite server queues.
Boxma et al. (Thu,) studied this question.