On the stability of a class of non-monotonic systems of parallel queues
Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the...
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Gespeichert in:
| Autor*in: |
Moyal, Pascal [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Discrete event dynamic systems - Springer US, 1991, 27(2016), 1 vom: 14. Sept., Seite 85-107 |
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| Übergeordnetes Werk: |
volume:27 ; year:2016 ; number:1 ; day:14 ; month:09 ; pages:85-107 |
| Links: |
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| DOI / URN: |
10.1007/s10626-016-0230-9 |
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OLC2027359176 |
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| 520 | |a Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. | ||
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10.1007/s10626-016-0230-9 doi (DE-627)OLC2027359176 (DE-He213)s10626-016-0230-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Moyal, Pascal verfasserin aut On the stability of a class of non-monotonic systems of parallel queues 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. Queueing systems Stochastic recursive sequences Stability Parallel queues Enthalten in Discrete event dynamic systems Springer US, 1991 27(2016), 1 vom: 14. Sept., Seite 85-107 (DE-627)130988766 (DE-600)1079508-X (DE-576)029154278 0924-6703 nnns volume:27 year:2016 number:1 day:14 month:09 pages:85-107 https://doi.org/10.1007/s10626-016-0230-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 27 2016 1 14 09 85-107 |
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10.1007/s10626-016-0230-9 doi (DE-627)OLC2027359176 (DE-He213)s10626-016-0230-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Moyal, Pascal verfasserin aut On the stability of a class of non-monotonic systems of parallel queues 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. Queueing systems Stochastic recursive sequences Stability Parallel queues Enthalten in Discrete event dynamic systems Springer US, 1991 27(2016), 1 vom: 14. Sept., Seite 85-107 (DE-627)130988766 (DE-600)1079508-X (DE-576)029154278 0924-6703 nnns volume:27 year:2016 number:1 day:14 month:09 pages:85-107 https://doi.org/10.1007/s10626-016-0230-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 27 2016 1 14 09 85-107 |
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10.1007/s10626-016-0230-9 doi (DE-627)OLC2027359176 (DE-He213)s10626-016-0230-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Moyal, Pascal verfasserin aut On the stability of a class of non-monotonic systems of parallel queues 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. Queueing systems Stochastic recursive sequences Stability Parallel queues Enthalten in Discrete event dynamic systems Springer US, 1991 27(2016), 1 vom: 14. Sept., Seite 85-107 (DE-627)130988766 (DE-600)1079508-X (DE-576)029154278 0924-6703 nnns volume:27 year:2016 number:1 day:14 month:09 pages:85-107 https://doi.org/10.1007/s10626-016-0230-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 27 2016 1 14 09 85-107 |
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10.1007/s10626-016-0230-9 doi (DE-627)OLC2027359176 (DE-He213)s10626-016-0230-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Moyal, Pascal verfasserin aut On the stability of a class of non-monotonic systems of parallel queues 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. Queueing systems Stochastic recursive sequences Stability Parallel queues Enthalten in Discrete event dynamic systems Springer US, 1991 27(2016), 1 vom: 14. Sept., Seite 85-107 (DE-627)130988766 (DE-600)1079508-X (DE-576)029154278 0924-6703 nnns volume:27 year:2016 number:1 day:14 month:09 pages:85-107 https://doi.org/10.1007/s10626-016-0230-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 27 2016 1 14 09 85-107 |
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10.1007/s10626-016-0230-9 doi (DE-627)OLC2027359176 (DE-He213)s10626-016-0230-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Moyal, Pascal verfasserin aut On the stability of a class of non-monotonic systems of parallel queues 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. Queueing systems Stochastic recursive sequences Stability Parallel queues Enthalten in Discrete event dynamic systems Springer US, 1991 27(2016), 1 vom: 14. Sept., Seite 85-107 (DE-627)130988766 (DE-600)1079508-X (DE-576)029154278 0924-6703 nnns volume:27 year:2016 number:1 day:14 month:09 pages:85-107 https://doi.org/10.1007/s10626-016-0230-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 27 2016 1 14 09 85-107 |
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Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. © Springer Science+Business Media New York 2016 |
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Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. © Springer Science+Business Media New York 2016 |
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Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system. © Springer Science+Business Media New York 2016 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2027359176</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503041402.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10626-016-0230-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2027359176</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10626-016-0230-9-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Moyal, Pascal</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the stability of a class of non-monotonic systems of parallel queues</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media New York 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. 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