The busy period of an M/G/1 queue with customer impatience

Onno Boxma, David Perry, Wolfgang Stadje, Shelley Zacks

Research output: Contribution to journalArticlepeer-review


We consider an M/G/1 queue in which an arriving customer does not enter the system whenever its virtual waiting time, i.e. the amount of work seen upon arrival, is larger than a certain random patience time. We determine the busy period distribution for various choices of the patience time distribution. The main cases under consideration are exponential patience and a discrete patience distribution.

Original languageEnglish
Pages (from-to)130-145
Number of pages16
JournalJournal of Applied Probability
Issue number1
StatePublished - Mar 2010


  • Busy period
  • Impatience
  • M/G/1 queue
  • Virtual waiting time

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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