Queueing Systems

, Volume 61, Issue 1, pp 37–63 | Cite as

On a generic class of two-node queueing systems

  • Ivo Adan
  • Michel Mandjes
  • Werner Scheinhardt
  • Elena Tzenova
Open Access
Article

Abstract

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics.

Keywords

Large-deviation Markovian fluid source Tail asymptotics Tandem queue 

Mathematics Subject Classification (2000)

60K25 90B22 

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Ivo Adan
    • 1
    • 2
  • Michel Mandjes
    • 3
    • 4
    • 2
  • Werner Scheinhardt
    • 4
    • 5
  • Elena Tzenova
    • 2
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.EurandomEindhovenThe Netherlands
  3. 3.Korteweg-de Vries InstituteUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.CWIAmsterdamThe Netherlands
  5. 5.Faculty of Electrical Engineering, Mathematics, and Computer ScienceUniversity of TwenteEnschedeThe Netherlands

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