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On Positive Recurrence of Mn/GI/1/∞ Model
Version 1
: Received: 23 September 2023 / Approved: 25 September 2023 / Online: 25 September 2023 (05:37:40 CEST)
A peer-reviewed article of this Preprint also exists.
Veretennikov, A. On Positive Recurrence of the Mn/GI/1/∞ Model. Mathematics 2023, 11, 4514. Veretennikov, A. On Positive Recurrence of the Mn/GI/1/∞ Model. Mathematics 2023, 11, 4514.
Abstract
Positive recurrence for a single-server queueing system is established under generalised intensity conditions of service which does not assume existence of the density distribution function of service but a certain integral type lower bound as a sufficient condition. Positive recurrence implies existence of the invariant distribution and a guaranteed slow convergence to it in the total variation metric.
Keywords
M/GI/1/∞; positive recurrence; general service distribution function
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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