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