Queueing Systems

, Volume 54, Issue 2, pp 111–120 | Cite as

Large buffer asymptotics for generalized processor sharing queues with Gaussian inputs

  • Krzysztof Dębicki
  • Miranda van Uitert


In this paper we derive large-buffer asymptotics for a two-class Generalized Processor Sharing (GPS) model. We assume both classes to have Gaussian characteristics. We distinguish three cases depending on whether the GPS weights are above or below the average rate at which traffic is sent. First, we calculate exact asymptotic upper and lower bounds, then we calculate the logarithmic asymptotics, and finally we show that the decay rates of the upper and lower bound match. We apply our results to two special Gaussian models: the integrated Gaussian process and the fractional Brownian motion. Finally we derive the logarithmic large-buffer asymptotics for the case where a Gaussian flow interacts with an on-off flow.


Large-buffer asymptotics Gaussian traffic Generalized processor sharing Communication networks Differentiated services 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of WrocławWrocławPoland
  2. 2.Netherlands Cancer InstituteAmsterdamThe Netherlands

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