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Derivation of Kolmogorov-Chapman type equations with Fokker-Planck operator. (Russian. English summary) Zbl 1446.05002
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
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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
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