On the distribution of queueing-related quantities with Lévy inputs

This paper investigates several queueing-related quantities associated with workload processes driven by spectrally one-sided Lévy inputs. We derive explicit expressions for the workload correlation function, the busy-period survival function, and the distribution of the running infimum of the workload process. The analysis is based on an exact expression for the transient workload distribution, which also enables a direct study of the structural properties of the correlation function. In the spectrally negative case, we further derive the joint distribution of the stationary workloads in a Lévy-driven tandem queue. The results are illustrated through explicit examples, with particular emphasis on Brownian motion with drift and compound Poisson input with exponential jumps.