Stability analysis of cascade networks via fluid models

Rosario Delgado*, Evsey Morozov

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

In this work, the fluid approach methodology is first applied to find a sufficient stability condition for a two-station cascade network: customers that are awaiting service at the first queue can move to the second station, whenever it is free, to be served there immediately, but the opposite is not allowed. Each station is fed by a renewal input with general i.i.d. inter-arrival times and general i.i.d. service times (possibly different in the two stations). Then we extend the stability analysis to cascade networks with an arbitrary number N of stations and find a sufficient stability condition. In such networks, an awaiting customer from the queue j>N-1 jumps to station j+1 if free, to be served there. Finally, we obtain a necessary condition for stability of the N-station cascade network, which matches the sufficient condition when N=2.

Original languageEnglish
Pages (from-to)39-54
Number of pages16
JournalPerformance Evaluation
Volume82
DOIs
Publication statusPublished - Dec 2014

Keywords

  • Cascade queueing network Stability Fluid limit approach Lyapunov function

Fingerprint

Dive into the research topics of 'Stability analysis of cascade networks via fluid models'. Together they form a unique fingerprint.

Cite this