Sojourn Time Distribution in Fluid Queues

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.
Original languageEnglish
Title of host publicationQueueing Theory and Network Applications
Subtitle of host publication14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings
PublisherSpringer
Pages295-313
Volume11688
ISBN (Print)978-3-030-27180-0
Publication statusPublished - 27 Aug 2019

Fingerprint

Fluid Queue
Sojourn Time
Buffer
Fluid Flow
Laplace-Stieltjes Transform
Stationary Distribution
Instant
Transform
Numerical Examples
Model

Keywords

  • Markov-modulated fluid flow
  • Sojourn time
  • Laplace-Stieljes transform

Cite this

Deiana, E., Remiche, M-A., & Latouche, G. (2019). Sojourn Time Distribution in Fluid Queues. In Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings (Vol. 11688, pp. 295-313). Springer.
Deiana, Eleonora ; Remiche, Marie-Ange ; Latouche, Guy. / Sojourn Time Distribution in Fluid Queues. Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings. Vol. 11688 Springer, 2019. pp. 295-313
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title = "Sojourn Time Distribution in Fluid Queues",
abstract = "We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.",
keywords = "Markov-modulated fluid flow, Sojourn time, Laplace-Stieljes transform",
author = "Eleonora Deiana and Marie-Ange Remiche and Guy Latouche",
note = "Best Student Paper Award",
year = "2019",
month = "8",
day = "27",
language = "English",
isbn = "978-3-030-27180-0",
volume = "11688",
pages = "295--313",
booktitle = "Queueing Theory and Network Applications",
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}

Deiana, E, Remiche, M-A & Latouche, G 2019, Sojourn Time Distribution in Fluid Queues. in Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings. vol. 11688, Springer, pp. 295-313.

Sojourn Time Distribution in Fluid Queues. / Deiana, Eleonora; Remiche, Marie-Ange; Latouche, Guy.

Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings. Vol. 11688 Springer, 2019. p. 295-313.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

TY - GEN

T1 - Sojourn Time Distribution in Fluid Queues

AU - Deiana, Eleonora

AU - Remiche, Marie-Ange

AU - Latouche, Guy

N1 - Best Student Paper Award

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Y1 - 2019/8/27

N2 - We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.

AB - We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.

KW - Markov-modulated fluid flow

KW - Sojourn time

KW - Laplace-Stieljes transform

M3 - Conference contribution

SN - 978-3-030-27180-0

VL - 11688

SP - 295

EP - 313

BT - Queueing Theory and Network Applications

PB - Springer

ER -

Deiana E, Remiche M-A, Latouche G. Sojourn Time Distribution in Fluid Queues. In Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings. Vol. 11688. Springer. 2019. p. 295-313