4 research outputs found
Overlap Times in the Queue
Overlap times have been studied as a way of understanding the time of
interaction between customers in a service facility. Most of the previous
analysis relies on the single jump assumption for arrivals, which implies the
queue increases by one for each arrival epoch. In this paper, we relax the
single arrival assumption and explore the impact of having batch arrivals.
Unfortunately, with batch arrivals it is not clear how one measures an overlap
time between batches of customers. Thus, we develop two ways of capturing the
notion of an overlap time in a batch setting and derive exact results in the
infinite server queue with batch arrivals. Finally, we derive new results for
analyzing overlap times of more than two batches