In this paper, we investigate overlap times in a two-dimensional infinite
server tandem queue. Specifically, we analyze the amount of time that a pair of
customers spend overlapping in any station of the two dimensional tandem
network. We assume that both stations have independent and identically
distributed exponential service times with the same rate parameter μ. Our
main contribution is the derivation of the joint tail distribution, the two
marginal tail probabilities, the moments of the overlap times and the tail
distribution of the sum of the overlap times in both stations. Our results shed
light on how customers overlap downstream in serial queueing systems