Performance analysis of a complex queueing system with vacations in random environment

This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing t...
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Autor*in:	Jianjun Li [verfasserIn] Liwei Liu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Übergeordnetes Werk:	In: Advances in Mechanical Engineering - SAGE Publishing, 2009, 9(2017)
Übergeordnetes Werk:	volume:9 ; year:2017

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1177/1687814017714167

Katalog-ID:	DOAJ045803781

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spelling	10.1177/1687814017714167 doi (DE-627)DOAJ045803781 (DE-599)DOAJdb3e106b117e4f9ebf70727933eecbb7 DE-627 ger DE-627 rakwb eng TJ1-1570 Jianjun Li verfasserin aut Performance analysis of a complex queueing system with vacations in random environment 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples. Mechanical engineering and machinery Liwei Liu verfasserin aut In Advances in Mechanical Engineering SAGE Publishing, 2009 9(2017) (DE-627)603487076 (DE-600)2501620-9 16878140 nnns volume:9 year:2017 https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/article/db3e106b117e4f9ebf70727933eecbb7 kostenfrei https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/toc/1687-8140 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2017
allfields_unstemmed	10.1177/1687814017714167 doi (DE-627)DOAJ045803781 (DE-599)DOAJdb3e106b117e4f9ebf70727933eecbb7 DE-627 ger DE-627 rakwb eng TJ1-1570 Jianjun Li verfasserin aut Performance analysis of a complex queueing system with vacations in random environment 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples. Mechanical engineering and machinery Liwei Liu verfasserin aut In Advances in Mechanical Engineering SAGE Publishing, 2009 9(2017) (DE-627)603487076 (DE-600)2501620-9 16878140 nnns volume:9 year:2017 https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/article/db3e106b117e4f9ebf70727933eecbb7 kostenfrei https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/toc/1687-8140 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2017
allfieldsGer	10.1177/1687814017714167 doi (DE-627)DOAJ045803781 (DE-599)DOAJdb3e106b117e4f9ebf70727933eecbb7 DE-627 ger DE-627 rakwb eng TJ1-1570 Jianjun Li verfasserin aut Performance analysis of a complex queueing system with vacations in random environment 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples. Mechanical engineering and machinery Liwei Liu verfasserin aut In Advances in Mechanical Engineering SAGE Publishing, 2009 9(2017) (DE-627)603487076 (DE-600)2501620-9 16878140 nnns volume:9 year:2017 https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/article/db3e106b117e4f9ebf70727933eecbb7 kostenfrei https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/toc/1687-8140 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2017
allfieldsSound	10.1177/1687814017714167 doi (DE-627)DOAJ045803781 (DE-599)DOAJdb3e106b117e4f9ebf70727933eecbb7 DE-627 ger DE-627 rakwb eng TJ1-1570 Jianjun Li verfasserin aut Performance analysis of a complex queueing system with vacations in random environment 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples. Mechanical engineering and machinery Liwei Liu verfasserin aut In Advances in Mechanical Engineering SAGE Publishing, 2009 9(2017) (DE-627)603487076 (DE-600)2501620-9 16878140 nnns volume:9 year:2017 https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/article/db3e106b117e4f9ebf70727933eecbb7 kostenfrei https://doi.org/10.1177/1687814017714167 kostenfrei https://doaj.org/toc/1687-8140 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2017
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callnumber-first	T - Technology
author	Jianjun Li
spellingShingle	Jianjun Li misc TJ1-1570 misc Mechanical engineering and machinery Performance analysis of a complex queueing system with vacations in random environment
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topic_title	TJ1-1570 Performance analysis of a complex queueing system with vacations in random environment
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title	Performance analysis of a complex queueing system with vacations in random environment
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title_full	Performance analysis of a complex queueing system with vacations in random environment
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title_sort	performance analysis of a complex queueing system with vacations in random environment
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title_auth	Performance analysis of a complex queueing system with vacations in random environment
abstract	This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples.
abstractGer	This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples.
abstract_unstemmed	This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i , i = 1 , 2 , … , n , customers are served one by one. Whenever the system becomes empty at a service completion instant, the server starts a vacation, causing the system to move to vacation phase. When a vacation ends, if the system is empty, another begins. Otherwise, the system moves from the vacation phase to some operative phase i with probability q i , i = 1 , 2 , … , n . Using the method of probability generating function, we obtain the distribution for the steady-state queue length at arbitrary epoch. We also derive the distributions for the stationary sojourn time and the length of the server’s working time in a service cycle, respectively. Finally, we present some special cases and numerical examples.
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title_short	Performance analysis of a complex queueing system with vacations in random environment
url	https://doi.org/10.1177/1687814017714167 https://doaj.org/article/db3e106b117e4f9ebf70727933eecbb7 https://doaj.org/toc/1687-8140
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