Quasi-Product Forms for Lévy-Driven Fluid Networks

K. Debicki, A.B. Dieker, T. Rolski

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)

Abstract

We study stochastic tree fluid networks driven by a multidimensional Lévy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy periods, and the idle periods. To investigate these fluid networks, we relate the above three quantities to fluctuations of the input Lévy process by solving a multidimensional Skorokhod reflection problem. This leads to the analysis of the distribution of the componentwise maximums, the corresponding epochs at which they are attained, and the beginning of the first last-passage excursion. Using the notion of splitting times, we are able to find their Laplace transforms. It turns out that, if the components of the Lévy process are “ordered,��? the Laplace transform has a so-called quasi-product form. The theory is illustrated by working out special cases, such as tandem networks and priority queues.
Original languageUndefined
Article number10.1287/moor.1070.0259
Pages (from-to)629-647
Number of pages19
JournalMathematics of operations research
Volume32
Issue number1/3
DOIs
Publication statusPublished - Aug 2007

Keywords

  • EWI-7602
  • MSC-60K25
  • IR-63586
  • MSC-90B05
  • METIS-241557
  • MSC-60G51

Cite this

Debicki, K., Dieker, A. B., & Rolski, T. (2007). Quasi-Product Forms for Lévy-Driven Fluid Networks. Mathematics of operations research, 32(1/3), 629-647. [10.1287/moor.1070.0259]. https://doi.org/10.1287/moor.1070.0259