A Lévy input fluid queue with input and workload regulation

Z.B. Palmowski, M. Vlasiou, B. Zwart

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Abstract

We consider a controlled queuing model with Lévy input. The controls take place at random times. They involve the current workload and the input processes and may also depend on whether the workload process has reached certain critical values since the last control epoch. We propose a solution strategy for deriving the steady-state distribution of this model which is based on recent advances in the fluctuation theory of spectrally one-sided Lévy process. We provide illustrative examples involving a clearing model, an inventory model, and a model for the TCP protocol. Keywords: Fluctuation theory; TCP model; Inventory model; Clearing model; Workload; Scale functions
Original languageEnglish
Pages (from-to)21-36
JournalQueueing Systems: Theory and Applications
Volume76
Issue number1
DOIs
Publication statusPublished - 2014

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Fluid Queue
Workload
Fluids
Fluctuations (theory)
Inventory Model
Scale Function
Queuing Model
Model
Steady-state Distribution
Critical value
Queue

Cite this

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A Lévy input fluid queue with input and workload regulation. / Palmowski, Z.B.; Vlasiou, M.; Zwart, B.

In: Queueing Systems: Theory and Applications, Vol. 76, No. 1, 2014, p. 21-36.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - We consider a controlled queuing model with Lévy input. The controls take place at random times. They involve the current workload and the input processes and may also depend on whether the workload process has reached certain critical values since the last control epoch. We propose a solution strategy for deriving the steady-state distribution of this model which is based on recent advances in the fluctuation theory of spectrally one-sided Lévy process. We provide illustrative examples involving a clearing model, an inventory model, and a model for the TCP protocol. Keywords: Fluctuation theory; TCP model; Inventory model; Clearing model; Workload; Scale functions

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JO - Queueing Systems: Theory and Applications

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