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 queuing model with the workload evolving between consecutive i.i.d. exponential timers $\{e_q^{(i)}\}_{i=1,2,\ldots}$ according to a spectrally positive Lévy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the Lévy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment i of the Lévy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of Lévy processes, to workload and queuing models.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages17
Publication statusPublished - 2011

Publication series

NameReport Eurandom
Volume2011033
ISSN (Print)1389-2355

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Cite this

Palmowski, Z. B., Vlasiou, M., & Zwart, B. (2011). A Lévy input fluid queue with input and workload regulation. (Report Eurandom; Vol. 2011033). Eindhoven: Eurandom.