Quasi-stationary analysis for queues with temporary overload

S.K. Cheung, Richardus J. Boucherie, R. Núñez-Queija

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Motivated by the high variation in transmission rates for document transfer in the Internet and file down loads from web servers, we study the buffer content in a queue with a fluctuating service rate. The fluctuations are assumed to be driven by an independent stochastic process. We allow the queue to be overloaded in some of the server states. In all but a few special cases, either exact analysis is not tractable, or the dependence of system performance in terms of input parameters (such as the traffic load) is hidden in complex or implicit characterizations. Various asymptotic regimes have been considered to develop insightful approximations. In particular, the so-called quasistationary approximation has proven extremely useful under the assumption of uniform stability. We refine the quasi-stationary analysis to allow for temporary instability, by studying the “effective system load‿ which captures the effect of accumulated work during periods in which the queue is unstable.
Original languageUndefined
Title of host publicationProceedings of the 22nd International Teletraffic Congress (ITC)
Place of PublicationUSA
Number of pages8
ISBN (Print)978-1-4244-8837-7
Publication statusPublished - 2010
Event22nd International Teletraffic Congress 2010 - Science Park Amsterdam, Amsterdam, Netherlands
Duration: 7 Sept 20109 Sept 2010
Conference number: 22

Publication series

PublisherIEEE Communications Society


Conference22nd International Teletraffic Congress 2010
Abbreviated titleITC 2010
Internet address


  • METIS-271098
  • IR-74327
  • Effective load
  • Recovery time
  • EWI-18668
  • Fluid queue
  • Fluctuating rates
  • Markovian random environment
  • Excess load
  • Quasi-stationary analysis

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