Derivation of Kolmogorov -- Chapman type equations with Fokker -- Planck operator
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 90-107.

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In this paper we obtain the differential equation of the type Kolmogorov – Chapman with differential operator of the Fokker – Planck, having theoretical and practical value in the differential equations theory. Equations concerning non-stationary and stationary characteristics of the number of applications obtained for a class of Queuing systems (QS) with an infinite storage device, one service device with exponential service, the input of which is supplied twice stochastic a Poisson flow whose intensity is a random diffusion process with springy boundaries and a non-zero drift coefficient. Service systems with diffusion intensity of the input flow are used for modeling of global computer networks nodes.
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D. B. Prokopieva; T. А. Zhuk; N. I. Golovko. Derivation of Kolmogorov -- Chapman type equations with Fokker -- Planck operator. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 90-107. http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a9/

[1] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982

[2] N. Sh. Kremer, Issledovanie operatsii v ekonomike, YuRAIT, M., 2010

[3] B. V. Gnedenko, I.N. Kovalenko, Vvedenie v teoriyu massovogo obsluzhivaniya, Nauka, M., 1987 | MR

[4] D. Kouzi, Kompyuternye seti. Kniga 2: Networking Essentials, Diasoft, Kiev, 1999

[5] M. Levin, Kompyuternye seti. Ustroistvo, podklyuchenie i ispolzovanie., Overlei, M., 2000

[6] N. I. Golovko, V. O. Karetnik, V. E. Tanin, I. I. Safonyuk, “Issledovanie modelei sistem massovogo obsluzhivaniya v informatsionnykh setyakh”, Sibirskii zhurnal industrialnoi matematiki, 2(34) (2008), 50–64 | Zbl

[7] A. D. Crescenzo, “Diffusion approximation to a queueing system with time-dependent arrival and service rates”, Queueing Systems, 14(19) (1995), 41–62 | DOI | MR

[8] R. Atar, “A diffusion model of scheduling control in queueing systems with many servers”, Ann. Appl. Probab, 15(1B) (2005), 820–852 | DOI | MR | Zbl

[9] M. Miyazawa, “Diffusion approximation for stationary analysis of queues and their networks: a review”, Journal of the Operations Research Society of Japan, 58(1) (2015), 104–148 | DOI | MR | Zbl

[10] D. B. Prokopeva, T. A. Zhuk, N. I. Golovko, “Vyvod uravnenii dlya sistem massovogo obsluzhivaniya s diffuzionnoi intensivnostyu vkhodnogo potoka i nulevym koeffitsientom snosa”, Izvestiya KGTU, 46 (2017), 184–193

[11] L. Kleinrok, Teoriya massovogo obsluzhivaniya, Mashinostroenie, M., 1979

[12] A. T. Barucha-Rid, Elementy teorii markovskikh protsessov i ikh prilozheniya, Nauka, M., 1969

[13] B. V. Gnedenko, Kurs teorii veroyatnostei, Nauka, M., 1988 | MR

[14] I. N. Bekman, Matematika diffuzii, uchebnoe posobie, OntoPrint, M., 2016