Asymptotics of subexponential max plus networks: The stochastic event graph case

François Baccelli, Marc Lelarge, Serguei Foss

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We calculate the exact tail asymptotics of stationary response times for open stochastic event graphs, in the irreducible and reducible cases. These networks admit a representation as (max, plus)-linear systems in a random medium. We study the case of renewal input and i.i.d. service times with subexponen-tial distributions. We show that the stationary response times have tail asymptotics of the same order as the integrated tail of service times. The mutiplicative constants only involve the intensity of the arrival process and the (max, plus)-Lyapunov exponents of the sequence of (max, plus)-matrices.

Original languageEnglish
Pages (from-to)75-96
Number of pages22
JournalQueueing Systems
Volume46
Issue number1-2
Publication statusPublished - Jan 2004

Keywords

  • (max, plus)-network
  • Heavy tail
  • Integrated tail
  • Open queueing network
  • Stochastic event graph
  • Subexponential random variable
  • Tandem queue
  • Veraverbeke's theorem

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