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Contents of PMS, Vol. 36, Fasc. 2,
pages 279 - 293
 

GI/GI/1 QUEUES WITH INFINITE MEANS OF SERVICE TIME AND INTERARRIVAL TIME

Władysław Szczotka

Abstract: The main results deal with the GI/GI/1 queues with infinite means of the service times and interarrival times. Theorem 3.1 gives an asymptotic, in a heavy traffic situation, of the sequence of waiting times of the consecutive customers. Theorem 4.1 gives an asymptotic of stationary waiting times in a heavy traffic situation. In a special case, the asymptotic stationary waiting times have an exponential distribution (Corollary 4.1).

2010 AMS Mathematics Subject Classification: Primary: 60K25; Secondary: 60F17, 60G99.

Keywords and phrases: Lévy process, stable distribution, GI/GI /1 queueing system, heavy traffic, stationary waiting time, tightness.

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