A tandem fluid network with Lévy input in heavy traffic

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of Lévy input, covering compound Poisson, α-stable Lévy motion (with 1 < α < 2), and Brownian motion. In our analysis, we separately deal with Lévy input processes with increments that have finite and infinite variance. A distinguishing feature of this paper is that we do not only consider the usual heavy traffic regime, in which the load at one of the nodes goes to unity, but also a regime in which we simultaneously let the load of both servers tend to one, which, as it turns out, leads to entirely different heavy traffic asymptotics. Numerical experiments indicate that under specific conditions the resulting simultaneous heavy traffic approximation significantly outperforms the usual heavy traffic approximation.