Tails in generalized Jackson networks with subexponential service-time distributions

François Baccelli, Serguei Foss, Marc Lelarge

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We give the exact asymptotics of the tail of the stationary maximal dater in generalized Jackson networks with subexponential service times. This maximal dater, which is an analogue of the workload in an isolated queue, gives the time taken to clear all customers present at some time t when stopping all arrivals that take place later than t. We use the property that a large deviation of the maximal dater is caused by a single large service time at a single station at some time in the distant past of t, in conjunction with fluid limits of generalized Jackson networks, to derive the relevant asymptotics in closed form. © Applied Probability Trust 2005.

Original languageEnglish
Pages (from-to)513-530
Number of pages18
JournalJournal of Applied Probability
Volume42
Issue number2
DOIs
Publication statusPublished - Jun 2005

Keywords

  • Fluid limit
  • Generalized Jackson network
  • Heavy tail
  • Integrated tail
  • Subexponential random variable
  • Veraverbeke's theorem

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