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Contents of PMS, Vol. 27, Fasc. 1,
pages 109 - 123
 

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.

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