A tandem fluid network with Lévy input in heavy traffic

D.T. Koops, O.J. Boxma, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of Lévy input, covering compound Poisson, (Formula presented.)-stable Lévy motion (with (Formula presented.)), and Brownian motion. In our analysis, we separately deal with Lévy input processes with increments that have finite and infinite variance. A distinguishing feature of this paper is that we do not only consider the usual heavy traffic regime, in which the load at one of the nodes goes to unity, but also a regime in which we simultaneously let the load of both servers tend to one, which, as it turns out, leads to entirely different heavy traffic asymptotics. Numerical experiments indicate that under specific conditions the resulting simultaneous heavy traffic approximation significantly outperforms the usual heavy traffic approximation.

Original languageEnglish
Pages (from-to)355–379
Number of pages25
JournalQueueing Systems: Theory and Applications
Volume84
Issue number3
DOIs
Publication statusPublished - 17 Sep 2016

Keywords

  • Fluid queue
  • Heavy tails
  • Heavy traffic
  • Lévy processes
  • Queueing theory
  • Steady-state distribution
  • Tandem queue

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