Markovian bulk-arriving queues with state-dependent control at idle time

A. Chen, E. Renshaw

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

This paper considers a Markovian bulk-arriving queue modified to allow both mass arrivals when the queue is idle and mass departures which allow for the possibility of removing the entire workload. Properties of queues which terminate when the server becomes idle are developed first, since these play a key role in later developments. Results for the case of mass arrivals, but no mass annihilation, are then constructed with specific attention being paid to recurrence properties, equilibrium queue-size structure, and waiting-time distribution. A closed-form expression for the expected queue size and its Laplace transform are also established. All of these results are then generalised to allow for the removal of the entire workload, with closed-form expressions being developed for the equilibrium size and waiting-time distributions.
LanguageEnglish
Pages499-524
Number of pages25
JournalAdvances in Applied Probability
Volume36
DOIs
Publication statusPublished - 2004

Fingerprint

Laplace transforms
Queue
Servers
Dependent
Waiting Time Distribution
Workload
Closed-form
Entire
Terminate
Annihilation
Recurrence
Laplace transform
Server

Keywords

  • equilibrium distribution
  • waiting-time distribution
  • recurrence
  • statistics
  • probability

Cite this

@article{f12e6650883448d4a48cd6f30cb29b01,
title = "Markovian bulk-arriving queues with state-dependent control at idle time",
abstract = "This paper considers a Markovian bulk-arriving queue modified to allow both mass arrivals when the queue is idle and mass departures which allow for the possibility of removing the entire workload. Properties of queues which terminate when the server becomes idle are developed first, since these play a key role in later developments. Results for the case of mass arrivals, but no mass annihilation, are then constructed with specific attention being paid to recurrence properties, equilibrium queue-size structure, and waiting-time distribution. A closed-form expression for the expected queue size and its Laplace transform are also established. All of these results are then generalised to allow for the removal of the entire workload, with closed-form expressions being developed for the equilibrium size and waiting-time distributions.",
keywords = "equilibrium distribution, waiting-time distribution, recurrence, statistics, probability",
author = "A. Chen and E. Renshaw",
year = "2004",
doi = "10.1239/aap/1086957583",
language = "English",
volume = "36",
pages = "499--524",
journal = "Advances in Applied Probability",
issn = "0001-8678",

}

Markovian bulk-arriving queues with state-dependent control at idle time. / Chen, A.; Renshaw, E.

In: Advances in Applied Probability, Vol. 36, 2004, p. 499-524.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Markovian bulk-arriving queues with state-dependent control at idle time

AU - Chen, A.

AU - Renshaw, E.

PY - 2004

Y1 - 2004

N2 - This paper considers a Markovian bulk-arriving queue modified to allow both mass arrivals when the queue is idle and mass departures which allow for the possibility of removing the entire workload. Properties of queues which terminate when the server becomes idle are developed first, since these play a key role in later developments. Results for the case of mass arrivals, but no mass annihilation, are then constructed with specific attention being paid to recurrence properties, equilibrium queue-size structure, and waiting-time distribution. A closed-form expression for the expected queue size and its Laplace transform are also established. All of these results are then generalised to allow for the removal of the entire workload, with closed-form expressions being developed for the equilibrium size and waiting-time distributions.

AB - This paper considers a Markovian bulk-arriving queue modified to allow both mass arrivals when the queue is idle and mass departures which allow for the possibility of removing the entire workload. Properties of queues which terminate when the server becomes idle are developed first, since these play a key role in later developments. Results for the case of mass arrivals, but no mass annihilation, are then constructed with specific attention being paid to recurrence properties, equilibrium queue-size structure, and waiting-time distribution. A closed-form expression for the expected queue size and its Laplace transform are also established. All of these results are then generalised to allow for the removal of the entire workload, with closed-form expressions being developed for the equilibrium size and waiting-time distributions.

KW - equilibrium distribution

KW - waiting-time distribution

KW - recurrence

KW - statistics

KW - probability

UR - http://dx.doi.org/10.1239/aap/1086957583

U2 - 10.1239/aap/1086957583

DO - 10.1239/aap/1086957583

M3 - Article

VL - 36

SP - 499

EP - 524

JO - Advances in Applied Probability

T2 - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

ER -