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001-es BibID:	BIBFORM077595
035-os BibID:	(Scopus)85061317310
Első szerző:	Lebedev, E.O.
Cím:	On Gaussian Approximation of Multi-Channel Networks with Input Flows of General Structure / E.O. Lebedev, H.V. Livinska, J. Sztrik
Dátum:	2019
ISSN:	1072-3374 1573-8795
Megjegyzések:	In this paper, a multi-channel queueing network with input flow of a general structure is considered. The multi-dimensional service process is introduced as the number of customers at network nodes. In the heavy-traffic regime, a functional limit theorem of diffusion approximation type is proved under the condition that the input flows converge to their limits in the uniform topology. A limit Gaussian process is constructed and its correlation characteristics are represented explicitly via the network parameters. A network with nonhomogeneous Poisson input flow is studied as a particular case of the general model, and a correspondent Gaussian limit process is built.
Tárgyszavak:	Műszaki tudományok Informatikai tudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk
Megjelenés:	Journal Of Mathematical Sciences. - 237 : 5 (2019), p. 684-691. -
További szerzők:	Livinska, H.V. Sztrik János (1953-) (informatikus, matematikus)
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat Szerző által megadott URL
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001-es BibID:	BIBFORM071718
Első szerző:	Livinska, H.V.
Cím:	Gaussian approximation of multichannel networks with different input structure / H. Livinska, E. Lebedev, J. Sztrik
Dátum:	2017
Megjegyzések:	Most studies in queueing theory are based on the assumption that an input flow is the standart Poisson one. However, in many situations there are deviations of real flows from the standart Poisson. For example, the rate of the flow can be dependent on time, but under certain natural conditions the flow remains close to a nonhomogeneous Poisson process. Such a situation occurs, in particular, when customers are arriving on the input from various sources, and the total flow is the sum of flows with low rate. In the work multi-channel queueing networks with different structure of an input are considered. At first, we consider an open queueing network with a nonhomogeneous Poisson flow of customers arriving from outside. Each node operates as a multi-channel queueing system. Once the service is completed at a node, the customer is transferred to another node or it leaves the network with correspondent probabilities. It is proved that under some heavy traffic assumptions on network parameters the multi-channel service process that is the number of customers at the nodes converges to a Gaussian process in the uniform topology. Correlation characteristics of the Gaussian process are written via network parameters in an explicit form. Secondly, we suppose the input flow in the network is a sum of low rate flows from many sources. For this case, a functional limit theorem on approximation of the service process by a Gaussian process is proved, provided that the appropriate convergence conditions of the total flow to the nonhomogeneous Poisson flow are satisfied. Finally, the previous model is replaced by a closed finite-source network. Each separate source generates a request and sends it to the input of the network. The source that sent the request for service is in standby mode and does not generate new one until its request service is completed. For such a network a similar result is formulated and proved on condition that the number of sources increases asymptotically.
Tárgyszavak:	Műszaki tudományok Informatikai tudományok előadáskivonat
Megjelenés:	XXXIV. International Seminar on Stability Problems for Stochastic Models 25-29 August 2017 Debrecen, Hungary : Book of abstracts. - p. 59.
További szerzők:	Lebedev, E.O. Sztrik János (1953-) (informatikus, matematikus)
Internet cím:	Szerző által megadott URL Intézményi repozitóriumban (DEA) tárolt változat
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001-es BibID:	BIBFORM071720
Első szerző:	Sztrik János (informatikus, matematikus)
Cím:	Recent results on finite source retrial queues with collisions / J. Sztrik, A. Nazarov, H. Livinska
Dátum:	2017
Tárgyszavak:	Műszaki tudományok Informatikai tudományok előadáskivonat
Megjelenés:	XXXIV. International Seminar on Stability Problems for Stochastic Models 25-29 August 2017 Debrecen, Hungary : Book of abstracts. - p. 97.
További szerzők:	Nazarov, Anatoly Livinska, H.V.
Internet cím:	Szerző által megadott URL Intézményi repozitóriumban (DEA) tárolt változat
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