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GI/GI/1 queues with infinite means of service time and interarrival time

Szczotka W.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 2

279--293

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).