Sample-path large deviations for tandem queues with Gaussian inputs

M.R.H. Mandjes; Miranda van Uitert

Sample-path large deviations for tandem queues with Gaussian inputs

M.R.H. Mandjes, Miranda van Uitert

Stochastic Operations Research

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both modes scaled appropriately, Schilder's sample-path large deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs.

Original language	Undefined
Title of host publication	Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress (ITC-18)
Editors	J. Charzinski, R. Lehnert, P. Tran-Gia
Place of Publication	Amsterdam
Publisher	Elsevier
Pages	521-530
Number of pages	10
ISBN (Print)	978-0-444-51455-4
Publication status	Published - Aug 2003
Event	18th International Teletraffic Congress 2003: Providing QoS in Heterogeneous Environments - Berlin, Germany Duration: 31 Aug 2003 → 5 Sept 2003 Conference number: 18 https://itc-conference.org/congresses/itc18.html

Publication series

Name	Teletraffic Science and Engineering
Publisher	Elsevier
Volume	5a

Conference

Conference	18th International Teletraffic Congress 2003
Abbreviated title	ITC 2003
Country/Territory	Germany
City	Berlin
Period	31/08/03 → 5/09/03
Internet address	https://itc-conference.org/congresses/itc18.html

Keywords

METIS-213614
EWI-17788
IR-71047

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Cite this

Mandjes, M. R. H., & van Uitert, M. (2003). Sample-path large deviations for tandem queues with Gaussian inputs. In J. Charzinski, R. Lehnert, & P. Tran-Gia (Eds.), Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress (ITC-18) (pp. 521-530). (Teletraffic Science and Engineering; Vol. 5a). Elsevier. http://eprints.eemcs.utwente.nl/secure2/17788/01/2003-28MandjesUitert-ITC.pdf

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title = "Sample-path large deviations for tandem queues with Gaussian inputs",

abstract = "We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both modes scaled appropriately, Schilder's sample-path large deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs.",

keywords = "METIS-213614, EWI-17788, IR-71047",

author = "M.R.H. Mandjes and {van Uitert}, Miranda",

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editor = "J. Charzinski and R. Lehnert and P. Tran-Gia",

booktitle = "Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress (ITC-18)",

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Mandjes, MRH & van Uitert, M 2003, Sample-path large deviations for tandem queues with Gaussian inputs. in J Charzinski, R Lehnert & P Tran-Gia (eds), Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress (ITC-18). Teletraffic Science and Engineering, vol. 5a, Elsevier, Amsterdam, pp. 521-530, 18th International Teletraffic Congress 2003, Berlin, Germany, 31/08/03. <http://eprints.eemcs.utwente.nl/secure2/17788/01/2003-28MandjesUitert-ITC.pdf>

Sample-path large deviations for tandem queues with Gaussian inputs. / Mandjes, M.R.H.; van Uitert, Miranda.
Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress (ITC-18). ed. / J. Charzinski; R. Lehnert; P. Tran-Gia. Amsterdam: Elsevier, 2003. p. 521-530 (Teletraffic Science and Engineering; Vol. 5a).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - van Uitert, Miranda

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N2 - We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both modes scaled appropriately, Schilder's sample-path large deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs.

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KW - EWI-17788

KW - IR-71047

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SN - 978-0-444-51455-4

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EP - 530

BT - Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress (ITC-18)

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