IJPAM: Volume 108, No. 2 (2016)

PHYSICAL AND MATHEMATICAL QUEUES IN
THE APPLIED QUEUING THEORY

Alexander Kirpichnikov$^1$, Anton Titovtsev$^2$
$^{1,2}$Kazan National Research Technological University
68, K. Marksa, Kazan, 420015, RUSSIA

Abstract. The problem of various types of queues arising in queuing systems is considered in the paper. The concept of a physical queue is introduced; universal mathematical formulas of the first and second moments of main discrete and continuous random variables characterizing behavior of physical queues for various models of mixed type queuing systems are obtained.

Received: May 12, 2016

Revised: May 12, 2016

Published: October 1, 2016

AMS Subject Classification: 60K25

Key Words and Phrases: physical queue, queue, quality of service (QoS), queuing system (QS)
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Bibliography

1
J.W. Cohen, Certain delay problems for a full availability trunk group loaded by two sources, Communication News, 16, No. 3 (1956), 105-113.

2
A.P.Kirpichnikov Prikladnaya teoriya massovogo obsluzhivaniya [Applied queuing theory], Publishing office of KSU Publ., Kazan (2008), In Russian.

3
A.P.Kirpichnikov Metody prikladnoy teorii massovogo obsluzhivaniya[Methods of applied queuing theory], Publishing office of KSU Publ., Kazan(2011), In Russian.

4
A.P. Kirpichnikov, A.S. Titovtsev, Open systems of multicomponent flowsdifferentiated service, Ciência e Técnica Vitivinıcola,29, No. 7 (2014), 108-122.

5
A. Kirpichnikov, A. Titovtsev, Mathematical model of a queuing system witharbitrary quantity of sources and size-limited queue, International Journal ofPure and Applied Mathematics, 106, No. 2 (2016), 649-661.

6
A. Kirpichnikov, A. Titovtsev, Mathematical model of open queuing system withfull set of memories, International Journal ofPure and Applied Mathematics, 107, No. 1 (2016), 139-143.

7
H. Takagi, Explicit delay distribution in first-come first-served M/M/m/K andM/M/m/K/n queues and mixed loss-delay system, International Journal ofPure and Applied Mathematics, 40, No. 2 (2007), 185-200.

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DOI: 10.12732/ijpam.v108i2.15 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 409 - 419


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