We analyze tail asymptotics of a two-node tandem queue with spectrally-positive Lévy input. A first focus lies in the tail probabilities of the type ¿(Q 1>¿ x,Q 2>(1¿¿)x), for ¿¿(0,1) and x large, and Q i denoting the steady-state workload in the ith queue. In case of light-tailed input, our analysis heavily uses the joint Laplace transform of the stationary buffer contents of the first and second queue; the logarithmic asymptotics can be expressed as the solution to a convex programming problem. In case of heavy-tailed input we rely on sample-path methods to derive the exact asymptotics. Then we specialize in the tail asymptotics of the downstream queue, again in case of both light-tailed and heavy-tailed Lévy inputs. It is also indicated how the results can be extended to tandem queues with more than two nodes.
Logistics (theme 3), Energy (theme 4)
Springer
Queueing Systems
Stochastics

Lieshout, P.M.D, & Mandjes, M.R.H. (2008). Asymptotic analysis of Lévy-driven tandem queues. Queueing Systems, 60(3-4), 203–226.