M/ph/1 queue with deterministic impatience time

Jerim Kim, Jeongsim Kim

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider an M/PH/1 queue with deterministic impa-tience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

Original languageEnglish
Pages (from-to)383-396
Number of pages14
JournalCommunications of the Korean Mathematical Society
Issue number2
StatePublished - 2013


  • Impatience time
  • Loss probability
  • M/ph/1 queue
  • Queue size distribution
  • Waiting time distribution
  • Workload


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