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Open Access Publications from the University of California

Scholarly Works (3 results)

  • Article
  • Peer Reviewed
UC San Diego Previously Published Works (2004)

This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches infinity. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffic diffusion approximation for a processor sharing queue.

    Cover page: Invariant states and rates of convergence for a critical fluid model of a processor sharing queue
    • Article
    • Peer Reviewed
    UC San Diego Previously Published Works (2016)
    In this paper, we develop a new approach to studying the asymptotic behavior of fluid model solutions for critically loaded processor sharing queues. For this, we introduce a notion of relative entropy associated with measure-valued fluid model solutions. In contrast to the approach used in [12], which does not readily generalize to networks of processor sharing queues, we expect the approach developed in this paper to be more robust. Indeed, we anticipate that similar notions involving relative entropy may be helpful for understanding the asymptotic behavior of critical fluid model solutions for stochastic networks operating under various resource sharing protocols naturally described by measure-valued processes.
      Creative Commons 'BY-NC-ND' version 4.0 license
      • Article
      • Peer Reviewed
      UC San Diego Previously Published Works (2019)
        Cover page: Asymptotic behavior of a critical fluid model for a multiclass processor sharing queue via relative entropyCreative Commons 'BY-NC-ND' version 4.0 license
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