On the cycle maximum of mountains, dams and queues

Onno J. Boxma, David Perry

Research output: Contribution to journalArticlepeer-review


We determine the distribution of the maximum level of the workload in some queueing, dam, and storage processes. The models under consideration are the following. (i) The Markov mountain: a storage or dam model that alternates between exponentially distributed ON and OFF periods. The buffer content increases (decreases) at some state-dependent rate when ON (OFF). (ii) The semi-Markov mountain: as (i), but with generally distributed ON periods. (iii) The M/G/1 queue with various forms of customer impatience.

Original languageEnglish
Pages (from-to)2706-2720
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Issue number16-17
StatePublished - Jan 2009


  • Cycle maximum
  • Dam
  • M/G/1 queue
  • Storage process

ASJC Scopus subject areas

  • Statistics and Probability


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