Prokop’eva, D. B.; Zhuk, T. A.; Golovko, N. I. Derivation of Kolmogorov-Chapman type equations with Fokker-Planck operator. (Russian. English summary) Zbl 1446.05002 Dal’nevost. Mat. Zh. 20, No. 1, 90-107 (2020). Summary: 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. MSC: 05-04 Software, source code, etc. for problems pertaining to combinatorics 34A35 Ordinary differential equations of infinite order PDF BibTeX XML Cite \textit{D. B. Prokop'eva} et al., Dal'nevost. Mat. Zh. 20, No. 1, 90--107 (2020; Zbl 1446.05002) Full Text: MNR References: [1] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982 · Zbl 0514.60091 [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 [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 1224.90036 [7] A. D. Crescenzo, “Diffusion approximation to a queueing system with time-dependent arrival and service rates”, Queueing Systems, 14(19) (1995), 41-62 · Zbl 0826.60087 [8] R. Atar, “A diffusion model of scheduling control in queueing systems with many servers”, Ann. Appl. Probab, 15(1B) (2005), 820-852 · Zbl 1084.60053 [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 · Zbl 1367.90042 [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 [14] I. N. Bekman, Matematika diffuzii, uchebnoe posobie, OntoPrint, M., 2016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.