Systems and Means of Informatics

2025, Volume 35, Issue 3, pp 71-89

UNIMODALITY OF THE WEIGHTED SUM OF PARTIAL CRITERIA OF THE G/M/1 MODEL WITH UPDATING AND A TWO-THRESHOLD RED-LIKE ALGORITHM

  • Ya. M. Agalarov

Abstract

Currently, in addition to end-to-end congestion control mechanisms, RED-like (RED - Random Early Detection) queue management mechanisms are being actively implemented in routers in existing information networks. The paper considers a model of the G/M/1 queue system in which the queue is controlled by a two-threshold RED-like algorithm with probabilistic dumping of requests.
In the model under consideration, the decision to reset is made at the time of completion of the client service depending on the current queue length. Theoretically, the behavior of a weighted function of criteria (the intensity of the accepted customer flow, the average delay of served customers, the intensity of rejected customers at the entrance, the intensity of customers dropped from the queue, and the average downtime of the device) is studied when changing the value of the lower threshold parameter of the algorithm. A number of statements about the properties of particular criteria and the statement that the weighted function of particular criteria is unimodal in terms of the lower threshold parameter are proved. A simple rule for correcting the value of the lower threshold parameter is proposed which is guaranteed to find the maximum value of a weighted function of particular criteria.

[+] References (25)

[+] About this article