On Positive Recurrence of the M n / GI /1/ ∞ Model

Alexander Veretennikov ()
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Alexander Veretennikov: Kharkevich Institute for Information Transmission Problems, Moscow 127051, Russia

Mathematics, 2023, vol. 11, issue 21, 1-18

Abstract: Positive recurrence for a single-server queueing system is established under generalized service intensity conditions, without the assumption of the existence of a service density distribution function, but with a certain integral type lower bound as a sufficient condition. Positive recurrence implies the existence of the invariant distribution and a guaranteed slow convergence to it in the total variation metric.

Keywords: Mn/GI/1/?; positive recurrence; general service distribution function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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