Informatics and Applications
2019, Volume 13, Issue 1, pp 55-61
ON THE UNIMODALITY OF THE INCOME FUNCTION OF A TYPE G|M|s QUEUEING SYSTEM WITH CONTROLLED QUEUE
- Ya. M. Agalarov
- V. G. Ushakov
Abstract
The problem of maximizing the average income in a queuing system of type G|M|s on a set of pure
stationary threshold strategies with single point switching access restriction mode is considered. The income
function depends on the following parameters, measured in value units: the fee received for servicing requests, the
cost of maintenance of the device, the deduction of income for the delay applications in the queue, the penalty
for unserved applications. It is proved that the income function is unimodal on the set of considered threshold
strategies. An algorithm for calculating the optimal threshold value and the corresponding maximum value income
is proposed. The results of the computational experiment that illustrate the work of the proposed algorithm are
given.
[+] References (9)
- Welzl, M. 2005. Network congestion control. New York, NY
Wiley. 282 p.
- Zhernovyj, Ju. V. 2010. Reshenie zadach optimal'nogo sinteza dlya nekotorykh markovskikh modeley obsluzhivaniya
[Solution of optimum synthesis problem for some Markov
models of service]. Informatsionnye processy [Information
Processes] 10(3):257-274.
- Konovalov, M. G. 2013. Ob odnoy zadache optimal'nogo
upravleniya nagruzkoy na server [About one task of over-
load control]. Informatika i ee Primeneniya - Inform. Appl.
7(4):34-43.
- Agalarov, Ya. M. 2015. Porogovaya strategiya ogranicheniya
dostupa k resursam v sisteme massovogo obsluzhivaniya
M/D/1 s funktsiey shtrafov za nesvoevremennoe obsluzhivanie zayavok [The threshold strategy for restricting
access in the M/D/1 queueing system with penalty func-
tion for late service]. Informatika i ee Primeneniya - Inform.
Appl. 9(3):55-64.
- Grishunina, Y. B. 2015. Optimal control of queue in the M|G|1|to system with possibility of customer admission restriction. Automat. Rem. Contr. 76(3):433-445.
- Agalarov, Ya. M. 2017. Maksimizatsiya srednego statsio- narnogo dokhoda sistemy massovogo obsluzhivaniya tipa M/G/1 [Maximization of average stationary profit in M/G/1 queuing system]. Informatika i ee Primeneniya - Inform. Appl. 11(2):25-32.
- Agalarov, Ya. M., and V. S. Shorgin. 2017. Ob odnoy zadache maksimizatsii dokhoda sistemy massovogo ob- sluzhivaniya tipa G/M/1 s porogovym upravleniem oche- red'yu [About the problem of profit maximization in G/M/1 queuing systems with threshold control of the queue]. Informatika i ee Primeneniya - Inform. Appl. 11(4):55-64.
- Karlin, S. 1968. A first course in stochastic processes. New York - London: Academic Press. 502 p.
- Bocharov, P. P., and A. V. Pechinkin. 1995. Teoriya massovogo obsluzhivaniya [Queueing theory]. Moscow: RUDN. 529 p.
[+] About this article
Title
ON THE UNIMODALITY OF THE INCOME FUNCTION OF A TYPE G|M|s QUEUEING SYSTEM WITH CONTROLLED QUEUE
Journal
Informatics and Applications
2019, Volume 13, Issue 1, pp 55-61
Cover Date
2019-04-30
DOI
10.14357/19922264190108
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
multichannel queueing system; threshold management; maximizing income
Authors
Ya. M. Agalarov  and V. G. Ushakov , 
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
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
|