Informatics and Applications
2019, Volume 13, Issue 2, pp 2-6
PROOF OF THE UNIMODALITY OF THE OBJECTIVE FUNCTION IN M/M/N QUEUE WITH THRESHOLD-BASED CONGESTION CONTROL
- Ya. M. Agalarov
- M. G. Konovalov
Abstract
The problem of limiting the load in the system M/M/N/infinity is considered using a simple threshold strategy. In addition to the service time, each task is characterized by a deadline. Depending on the quality of service, the system receives either a fixed income or a penalty. The quality of control is determined by the marginal average income and the threshold value that maximizes this value is considered as optimal. Usually, it is much easier to find the optimal threshold if the objective function has a single maximum. The experimental results show the unimodality of the objective function for a wide class of arrival flows. However, there is no rigorous proof of this fact and in the paper, this gap is filled up for the Poisson arrivals. The proof is based on the results of the Markov chain theory and queueing theory.
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[+] About this article
Title
PROOF OF THE UNIMODALITY OF THE OBJECTIVE FUNCTION IN M/M/N QUEUE WITH THRESHOLD-BASED CONGESTION CONTROL
Journal
Informatics and Applications
2019, Volume 13, Issue 2, pp 2-6
Cover Date
2019-06-30
DOI
10.14357/19922264190201
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov chains; M/M/N/infinity system; congestion control; threshold control; deadline
Authors
Ya. M. Agalarov  and M. G. Konovalov
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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