DISTRIBUTIONS OF SUPREMA OF LÉVY PROCESSES VIA THE HEAVY
TRAFFIC INVARIANCE PRINCIPLE
W. Szczotka
W. A. Woyczyński
Abstract: We study the relationship between the distribution of the supremum functional
for a process with stationary, but not necessarily
independent increments, and the limiting distribution of an appropriately normalized
stationary waiting time for G/G/l queues in heavy traffic. As a by-product we obtain explicit
expressions for the distribution of in several special cases of Lévy processes.
2000 AMS Mathematics Subject Classification: 60K25, 60G10, 60G18, 60E07.
Key words and phrases: Lévy process, supremum, heavy traffic, queueing systems.