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This article is cited in 4 scientific papers (total in 4 papers)
Proof of the unimodality of the objective function in $M/M/N$ queue with threshold-based congestion control
Ya. M. Agalarov, M. G. Konovalov 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
Abstract:
The problem of limiting the load in the system $M/M/N/\infty$
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.
Keywords:
Markov chains, $M/M/N/\infty$ system, congestion control, threshold control, deadline.
Received: 20.02.2019
Citation:
Ya. M. Agalarov, M. G. Konovalov, “Proof of the unimodality of the objective function in $M/M/N$ queue with threshold-based congestion control”, Inform. Primen., 13:2 (2019), 2–6
Linking options:
https://www.mathnet.ru/eng/ia586 https://www.mathnet.ru/eng/ia/v13/i2/p2
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Abstract page: | 186 | Full-text PDF : | 112 | References: | 11 |
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