On the Cycle Maximum of Mountains, Dams and Queues

Onno J. Boxma and David Perry

Communications in Statistics - Theory and Methods, 2009, vol. 38, issue 16-17, 2706-2720

Abstract: 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.

Date: 2009
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DOI: 10.1080/03610910902936232

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