The M/G/1+G queue revisited

Onno Boxma, David Perry, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the end of his virtual sojourn time, whichever occurs first.

Original languageEnglish
Pages (from-to)207-220
Number of pages14
JournalQueueing Systems
Issue number3
StatePublished - Mar 2011

Bibliographical note

Funding Information:
Acknowledgements The research of O.J. Boxma was done within the framework of the BRICKS project and the European Network of Excellence Euro-NF. D. Perry gratefully acknowledges a visitor grant from the Netherlands Organisation for Scientific Research NWO. W. Stadje was supported by the Deutsche Forschungsgemeinschaft.


  • Balking
  • Busy period
  • Cycle maximum
  • Impatience
  • Number of customers
  • Reneging
  • Single-server queue
  • Workload

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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