Exponential single server queues in an interactive random environment

We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirect...
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Gespeichert in:

Autor*in:	Otten, Sonja [verfasserIn] Krenzler, Ruslan [verfasserIn] Daduna, Hans - 1947- [verfasserIn] Kruse, Karsten - 1984- [verfasserIn]
Körperschaften:	Technische Universität Hamburg Technische Universität Hamburg, Institut für Mathematik

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Rechteinformationen:	Open Access Namensnennung 4.0 International ; CC BY 4.0

Schlagwörter:	interactive random environment product form steady state Lyapunov functions throughput bounds production-inventory systems

Anmerkung:	Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik
Umfang:	Diagramme

Übergeordnetes Werk:	Enthalten in: Stochastic systems - Catonsville, MD : Soc., 2011, 00(2023), 00, Seite 1-49
Übergeordnetes Werk:	volume:00 ; year:2023 ; number:00 ; pages:1-49

Links:	Link aufrufen Link aufrufen Link aufrufen Link aufrufen

DOI / URN:	urn:nbn:de:gbv:830-882.0216392 10.15480/882.5042 10.1287/stsy.2023.0106

Katalog-ID:	1842675931

Internformat


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Indexfelder

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allfields	urn:nbn:de:gbv:830-882.0216392 urn 10.15480/882.5042 doi 10.1287/stsy.2023.0106 doi 11420/15118 hdl (DE-627)1842675931 (DE-599)KXP1842675931 DE-627 ger DE-627 rda eng 510: Mathematik Otten, Sonja verfasserin (DE-588)1147656983 (DE-627)1006415769 (DE-576)49594422X aut Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems DSpace Krenzler, Ruslan verfasserin (DE-588)1147427852 (DE-627)1006159800 (DE-576)495792330 aut Daduna, Hans 1947- verfasserin (DE-588)142010626 (DE-627)704119323 (DE-576)160661617 aut Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Stochastic systems Catonsville, MD : Soc., 2011 00(2023), 00, Seite 1-49 (DE-627)791050106 (DE-600)2778150-1 (DE-576)410017760 1946-5238 nnns volume:00 year:2023 number:00 pages:1-49 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0216392 Resolving-System kostenfrei https://doi.org/10.15480/882.5042 Resolving-System kostenfrei http://hdl.handle.net/11420/15118 Resolving-System kostenfrei https://doi.org/10.1287/stsy.2023.0106 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 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_602 GBV_ILN_2009 GBV_ILN_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 DSpace AR 00 2023 00 1-49 045F 510: Mathematik 23 01 0830 430888358X tuhh Elektronischer Volltext f z 14-04-23 23 01 0830 https://doi.org/10.15480/882.5042 LF 23 01 0830 tuhh 23 01 0830 tubdok
spelling	urn:nbn:de:gbv:830-882.0216392 urn 10.15480/882.5042 doi 10.1287/stsy.2023.0106 doi 11420/15118 hdl (DE-627)1842675931 (DE-599)KXP1842675931 DE-627 ger DE-627 rda eng 510: Mathematik Otten, Sonja verfasserin (DE-588)1147656983 (DE-627)1006415769 (DE-576)49594422X aut Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems DSpace Krenzler, Ruslan verfasserin (DE-588)1147427852 (DE-627)1006159800 (DE-576)495792330 aut Daduna, Hans 1947- verfasserin (DE-588)142010626 (DE-627)704119323 (DE-576)160661617 aut Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Stochastic systems Catonsville, MD : Soc., 2011 00(2023), 00, Seite 1-49 (DE-627)791050106 (DE-600)2778150-1 (DE-576)410017760 1946-5238 nnns volume:00 year:2023 number:00 pages:1-49 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0216392 Resolving-System kostenfrei https://doi.org/10.15480/882.5042 Resolving-System kostenfrei http://hdl.handle.net/11420/15118 Resolving-System kostenfrei https://doi.org/10.1287/stsy.2023.0106 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 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_602 GBV_ILN_2009 GBV_ILN_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 DSpace AR 00 2023 00 1-49 045F 510: Mathematik 23 01 0830 430888358X tuhh Elektronischer Volltext f z 14-04-23 23 01 0830 https://doi.org/10.15480/882.5042 LF 23 01 0830 tuhh 23 01 0830 tubdok
allfields_unstemmed	urn:nbn:de:gbv:830-882.0216392 urn 10.15480/882.5042 doi 10.1287/stsy.2023.0106 doi 11420/15118 hdl (DE-627)1842675931 (DE-599)KXP1842675931 DE-627 ger DE-627 rda eng 510: Mathematik Otten, Sonja verfasserin (DE-588)1147656983 (DE-627)1006415769 (DE-576)49594422X aut Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems DSpace Krenzler, Ruslan verfasserin (DE-588)1147427852 (DE-627)1006159800 (DE-576)495792330 aut Daduna, Hans 1947- verfasserin (DE-588)142010626 (DE-627)704119323 (DE-576)160661617 aut Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Stochastic systems Catonsville, MD : Soc., 2011 00(2023), 00, Seite 1-49 (DE-627)791050106 (DE-600)2778150-1 (DE-576)410017760 1946-5238 nnns volume:00 year:2023 number:00 pages:1-49 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0216392 Resolving-System kostenfrei https://doi.org/10.15480/882.5042 Resolving-System kostenfrei http://hdl.handle.net/11420/15118 Resolving-System kostenfrei https://doi.org/10.1287/stsy.2023.0106 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 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_602 GBV_ILN_2009 GBV_ILN_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 DSpace AR 00 2023 00 1-49 045F 510: Mathematik 23 01 0830 430888358X tuhh Elektronischer Volltext f z 14-04-23 23 01 0830 https://doi.org/10.15480/882.5042 LF 23 01 0830 tuhh 23 01 0830 tubdok
allfieldsGer	urn:nbn:de:gbv:830-882.0216392 urn 10.15480/882.5042 doi 10.1287/stsy.2023.0106 doi 11420/15118 hdl (DE-627)1842675931 (DE-599)KXP1842675931 DE-627 ger DE-627 rda eng 510: Mathematik Otten, Sonja verfasserin (DE-588)1147656983 (DE-627)1006415769 (DE-576)49594422X aut Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems DSpace Krenzler, Ruslan verfasserin (DE-588)1147427852 (DE-627)1006159800 (DE-576)495792330 aut Daduna, Hans 1947- verfasserin (DE-588)142010626 (DE-627)704119323 (DE-576)160661617 aut Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Stochastic systems Catonsville, MD : Soc., 2011 00(2023), 00, Seite 1-49 (DE-627)791050106 (DE-600)2778150-1 (DE-576)410017760 1946-5238 nnns volume:00 year:2023 number:00 pages:1-49 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0216392 Resolving-System kostenfrei https://doi.org/10.15480/882.5042 Resolving-System kostenfrei http://hdl.handle.net/11420/15118 Resolving-System kostenfrei https://doi.org/10.1287/stsy.2023.0106 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 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_602 GBV_ILN_2009 GBV_ILN_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 DSpace AR 00 2023 00 1-49 045F 510: Mathematik 23 01 0830 430888358X tuhh Elektronischer Volltext f z 14-04-23 23 01 0830 https://doi.org/10.15480/882.5042 LF 23 01 0830 tuhh 23 01 0830 tubdok
allfieldsSound	urn:nbn:de:gbv:830-882.0216392 urn 10.15480/882.5042 doi 10.1287/stsy.2023.0106 doi 11420/15118 hdl (DE-627)1842675931 (DE-599)KXP1842675931 DE-627 ger DE-627 rda eng 510: Mathematik Otten, Sonja verfasserin (DE-588)1147656983 (DE-627)1006415769 (DE-576)49594422X aut Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse 2023 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems DSpace Krenzler, Ruslan verfasserin (DE-588)1147427852 (DE-627)1006159800 (DE-576)495792330 aut Daduna, Hans 1947- verfasserin (DE-588)142010626 (DE-627)704119323 (DE-576)160661617 aut Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Stochastic systems Catonsville, MD : Soc., 2011 00(2023), 00, Seite 1-49 (DE-627)791050106 (DE-600)2778150-1 (DE-576)410017760 1946-5238 nnns volume:00 year:2023 number:00 pages:1-49 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0216392 Resolving-System kostenfrei https://doi.org/10.15480/882.5042 Resolving-System kostenfrei http://hdl.handle.net/11420/15118 Resolving-System kostenfrei https://doi.org/10.1287/stsy.2023.0106 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 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_602 GBV_ILN_2009 GBV_ILN_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 DSpace AR 00 2023 00 1-49 045F 510: Mathematik 23 01 0830 430888358X tuhh Elektronischer Volltext f z 14-04-23 23 01 0830 https://doi.org/10.15480/882.5042 LF 23 01 0830 tuhh 23 01 0830 tubdok
language	English
source	Enthalten in Stochastic systems 00(2023), 00, Seite 1-49 volume:00 year:2023 number:00 pages:1-49
sourceStr	Enthalten in Stochastic systems 00(2023), 00, Seite 1-49 volume:00 year:2023 number:00 pages:1-49
format_phy_str_mv	Article
building	23
institution	findex.gbv.de
selectbib_iln_str_mv	23@
topic_facet	interactive random environment product form steady state Lyapunov functions throughput bounds production-inventory systems
dewey-raw	510: Mathematik
isfreeaccess_bool	true
container_title	Stochastic systems
authorswithroles_txt_mv	Otten, Sonja @@aut@@ Krenzler, Ruslan @@aut@@ Daduna, Hans @@aut@@ Kruse, Karsten @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	791050106
dewey-sort	3510 MATHEMATIK
id	1842675931
language_de	englisch
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topic_title	510: Mathematik Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems DSpace
topic	ddc 510: Mathematik DSpace interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems
topic_unstemmed	ddc 510: Mathematik DSpace interactive random environment DSpace product form steady state DSpace Lyapunov functions DSpace throughput bounds DSpace production-inventory systems
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title_full	Exponential single server queues in an interactive random environment Sonja Otten, Ruslan Krenzler, Hans Daduna, Karsten Kruse
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title_sort	exponential single server queues in an interactive random environment
title_auth	Exponential single server queues in an interactive random environment
abstract	We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik
abstractGer	We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik
abstract_unstemmed	We consider exponential single server queues with state-dependent arrival and service rates that evolve under influences of external environments. The transitions of the queues are influenced by the environment’s state and the movements of the environment depend on the status of the queues (bidirectional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process, we prove separability for a large class of such interactive systems; that is, the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For nonseparable systems, we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of nonseparable systems by throughputs of related separable systems as upper and lower bound. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik
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title_short	Exponential single server queues in an interactive random environment
url	http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0216392 https://doi.org/10.15480/882.5042 http://hdl.handle.net/11420/15118 https://doi.org/10.1287/stsy.2023.0106
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GND_str_mv	Otten, Sonja Krenzler, Ruslan Daduna, H. Daduna, Hans Kruse, Karsten University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Institute of Mathematics (Hamburg) Institut E-10 Technische Universität Hamburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institut für Mathematik (Hamburg) Technische Universität Hamburg. Institut E-10 Technische Universität Hamburg. Institute of Mathematics Technische Universität Hamburg. Institut für Mathematik
GND_txt_mv	Otten, Sonja Krenzler, Ruslan Daduna, H. Daduna, Hans Kruse, Karsten University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Institute of Mathematics (Hamburg) Institut E-10 Technische Universität Hamburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institut für Mathematik (Hamburg) Technische Universität Hamburg. Institut E-10 Technische Universität Hamburg. Institute of Mathematics Technische Universität Hamburg. Institut für Mathematik
GND_txtF_mv	Otten, Sonja Krenzler, Ruslan Daduna, H. Daduna, Hans Kruse, Karsten University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Institute of Mathematics (Hamburg) Institut E-10 Technische Universität Hamburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institut für Mathematik (Hamburg) Technische Universität Hamburg. Institut E-10 Technische Universität Hamburg. Institute of Mathematics Technische Universität Hamburg. Institut für Mathematik
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