TIGHTNESS OF STATIONARY WAITING TIMES IN HEAVY TRAFFIC FOR
GI/GI/1 QUEUES WITH THICK TAILS
M. Czysto³owski
W. Szczotka
Abstract: Recently, a Heavy Traffic Invariance Principle was proposed by Szczotka and
Woyczyńiski to characterize the heavy traffic limiting distribution of normalized stationary
waiting times of G/G/l queues in terms of an appropriate convergence to a Lévy process. It
has two important assumptions. The first of them deals with a convergence to a Lévy process
of appropriate processes which is well investigated in the literature. The second one states
that the sequence of appropriate normalized stationary waiting times is tight. In the present
paper we characterize the tightness condition for the case of GI/GI/l queues in terms of the
first condition.
2000 AMS Mathematics Subject Classification: 60K25.
Key words and phrases: Lévy process, queueing systems, heavy traffic, stationary
waiting time, tightness.