On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling

A finite-capacity queueing model with the arrival stream of messages governed by the compound Poisson process and generally-distributed processing times is investigated. Whenever the system becomes empty (the server becomes idle), a number of deterministic independent vacations of equal length are i...

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Autores principales:	Wojciech M. Kempa, Kamil Ksiazek, Rafal Marjasz
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Discontinuous reception (DRX) multiple vacation policy queue-size distribution stochastic simulation transient state Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/83a5a4d6a7864c31a4234a46c63e4bb4
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id	oai:doaj.org-article:83a5a4d6a7864c31a4234a46c63e4bb4
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spelling	oai:doaj.org-article:83a5a4d6a7864c31a4234a46c63e4bb42021-11-18T00:07:41ZOn Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling2169-353610.1109/ACCESS.2021.3123897https://doaj.org/article/83a5a4d6a7864c31a4234a46c63e4bb42021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9591613/https://doaj.org/toc/2169-3536A finite-capacity queueing model with the arrival stream of messages governed by the compound Poisson process and generally-distributed processing times is investigated. Whenever the system becomes empty (the server becomes idle), a number of deterministic independent vacations of equal length are initialized as far as at least one message is detected in the accumulating buffer at the completion epoch of one of them. During vacations the service process is suspended completely, while after finishing the last vacation it restarts normally. Identifying Markov moments in the evolution of the system and using the Korolyuk’s potential method, the compact-form representation for the transient queue-size distribution conditioned by the initial buffer state is found in terms of its Laplace transform. The considered model has potential applications in modeling the energy saving LTE DRX mechanism. A detailed simulation and numerical study is attached.Wojciech M. KempaKamil KsiazekRafal MarjaszIEEEarticleDiscontinuous reception (DRX)multiple vacation policyqueue-size distributionstochastic simulationtransient stateElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 148374-148383 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Discontinuous reception (DRX) multiple vacation policy queue-size distribution stochastic simulation transient state Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Discontinuous reception (DRX) multiple vacation policy queue-size distribution stochastic simulation transient state Electrical engineering. Electronics. Nuclear engineering TK1-9971 Wojciech M. Kempa Kamil Ksiazek Rafal Marjasz On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling
description	A finite-capacity queueing model with the arrival stream of messages governed by the compound Poisson process and generally-distributed processing times is investigated. Whenever the system becomes empty (the server becomes idle), a number of deterministic independent vacations of equal length are initialized as far as at least one message is detected in the accumulating buffer at the completion epoch of one of them. During vacations the service process is suspended completely, while after finishing the last vacation it restarts normally. Identifying Markov moments in the evolution of the system and using the Korolyuk’s potential method, the compact-form representation for the transient queue-size distribution conditioned by the initial buffer state is found in terms of its Laplace transform. The considered model has potential applications in modeling the energy saving LTE DRX mechanism. A detailed simulation and numerical study is attached.
format	article
author	Wojciech M. Kempa Kamil Ksiazek Rafal Marjasz
author_facet	Wojciech M. Kempa Kamil Ksiazek Rafal Marjasz
author_sort	Wojciech M. Kempa
title	On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling
title_short	On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling
title_full	On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling
title_fullStr	On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling
title_full_unstemmed	On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling
title_sort	on time-dependent queue-size distribution in a model with finite buffer capacity and deterministic multiple vacations with applications to lte drx mechanism modeling
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/83a5a4d6a7864c31a4234a46c63e4bb4
work_keys_str_mv	AT wojciechmkempa ontimedependentqueuesizedistributioninamodelwithfinitebuffercapacityanddeterministicmultiplevacationswithapplicationstoltedrxmechanismmodeling AT kamilksiazek ontimedependentqueuesizedistributioninamodelwithfinitebuffercapacityanddeterministicmultiplevacationswithapplicationstoltedrxmechanismmodeling AT rafalmarjasz ontimedependentqueuesizedistributioninamodelwithfinitebuffercapacityanddeterministicmultiplevacationswithapplicationstoltedrxmechanismmodeling
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On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling

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