The stationary workload of the G/M/1 queue with impatient customers

Jongho Bae, Sunggon Kim

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We consider a G/M/1 queue in which the patience time of the customers is constant. The stationary distribution of the workload of the server, or the virtual waiting time, is derived by the level crossing argument. To this end, we obtain the expected downcrossings of a level in the workload process during a busy cycle and then the expected length of a busy cycle. For both the expectations, we use the dual property between the M/G/1 and G/M/1 queue.

Original languageEnglish
Pages (from-to)253-265
Number of pages13
JournalQueueing Systems
Issue number3
StatePublished - Mar 2010


  • G/M/1 queue
  • Impatient customers
  • Virtual waiting time
  • Workload


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