Explicit solutions for the steady state distributions in M/PH/1

L.Q. Liu, V.G. Kulkarni

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Scopus)


We consider an M/PH/1 queue with balking based on the workload. An arriving customer joins the queue and stays until served only if the system workload is below a fixed level at the time of arrival. The steady state workload distribution in such a system satisfies an integral equation. We derive a differential equation for Phase type service time distribution and we solve it explicitly, with Erlang, Hyper-exponential and Exponential distributions as special cases. We illustrate the results with numerical examples.
Original languageEnglish
Pages (from-to)251-260
JournalQueueing Systems
Issue number4
Publication statusPublished - 2006


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