Transient analysis of Lévy-driven tandem queues

This short communication considers a tandem queue fed by Lévy input. The main result concerns expressions for the Laplace transform of the transient workload in the downstream queue, under the condition that the system starts off empty. This expression greatly simplifies if the driving Lévy process is spectrally one-sided; in that situation the transform is given explicitly in terms of the Laplace exponent of the Lévy input.