Stability and structural properties of stochastic storage networks

Offer Kella*, Ward Whitt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with non-zero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

Original languageAmerican English
Pages (from-to)1169-1180
Number of pages12
JournalJournal of Applied Probability
Volume33
Issue number4
DOIs
StatePublished - Dec 1996

Keywords

  • Bounds
  • Fluid networks
  • Lévy process
  • Reflected process
  • Stability
  • Stationary increments
  • Stochastic order
  • Stochastically increasing
  • Tightness

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