Markovian bulk-arrival and bulk-service queues with state-dependent control

Chen, Anyue, Pollett, Phil, Li, Junping and Zhang, Hanjun (2010) Markovian bulk-arrival and bulk-service queues with state-dependent control. Queueing Systems, 64 3: 267-304. doi:10.1007/s11134-009-9162-5


Author Chen, Anyue
Pollett, Phil
Li, Junping
Zhang, Hanjun
Title Markovian bulk-arrival and bulk-service queues with state-dependent control
Journal name Queueing Systems   Check publisher's open access policy
ISSN 0257-0130
1572-9443
Publication date 2010-03
Sub-type Article (original research)
DOI 10.1007/s11134-009-9162-5
Volume 64
Issue 3
Start page 267
End page 304
Total pages 38
Place of publication New York, United States
Publisher Springer New York LLC
Collection year 2011
Language eng
Abstract We study a modified Markovian bulk-arrival and bulk-service queue incorporating state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated and the relationship with our queueing model is examined and exploited. Equilibrium behaviour is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored. opyright © 2011 Elsevier B.V. All rights reserved
Keyword Bulk-arrival and bulk-service queues
State-dependent control
Equilibrium distribution
Transient behaviour
Queue length distributions
Hitting times
Busy period distributions
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
 
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Created: Sun, 21 Feb 2010, 00:01:01 EST