On the cycle maximum of mountains, dams and queues

O.J. Boxma, D. Perry

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)2706-2720
JournalCommunications in Statistics. Part A, Theory and Methods
Volume38
Issue number16-17
DOIs
Publication statusPublished - 2009

Fingerprint

Queue
Cycle
M/G/1 Queue
Queueing
Alternate
Workload
Buffer
Customers
Decrease
Dependent
Model
Form

Cite this

@article{8a8849ef20a64431a5f39cdf2a6fdb13,
title = "On the cycle maximum of mountains, dams and queues",
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.",
author = "O.J. Boxma and D. Perry",
year = "2009",
doi = "10.1080/03610910902936232",
language = "English",
volume = "38",
pages = "2706--2720",
journal = "Communications in Statistics. Part A, Theory and Methods",
issn = "0361-0926",
publisher = "Taylor and Francis Ltd.",
number = "16-17",

}

On the cycle maximum of mountains, dams and queues. / Boxma, O.J.; Perry, D.

In: Communications in Statistics. Part A, Theory and Methods, Vol. 38, No. 16-17, 2009, p. 2706-2720.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - On the cycle maximum of mountains, dams and queues

AU - Boxma, O.J.

AU - Perry, D.

PY - 2009

Y1 - 2009

N2 - 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.

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.

U2 - 10.1080/03610910902936232

DO - 10.1080/03610910902936232

M3 - Article

VL - 38

SP - 2706

EP - 2720

JO - Communications in Statistics. Part A, Theory and Methods

JF - Communications in Statistics. Part A, Theory and Methods

SN - 0361-0926

IS - 16-17

ER -