On the cycle maximum of mountains, dams and queues

Onno J. Boxma; David Perry

doi:10.1080/03610910902936232

On the cycle maximum of mountains, dams and queues

Onno J. Boxma, David Perry

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2706-2720
Number of pages	15
Journal	Communications in Statistics - Theory and Methods
Volume	38
Issue number	16-17
DOIs	https://doi.org/10.1080/03610910902936232
State	Published - Jan 2009

Keywords

Cycle maximum
Dam
M/G/1 queue
Storage process

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610910902936232

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AB - 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.

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On the cycle maximum of mountains, dams and queues

Abstract

Keywords

ASJC Scopus subject areas

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