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Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

Dieter Claeys UGent, Koenraad Laevens UGent, Joris Walraevens UGent and Herwig Bruneel UGent (2010) MATHEMATICAL METHODS OF OPERATIONS RESEARCH. 72(1). p.1-23
abstract
Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation-i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
PERFORMANCE ANALYSIS, MULTISERVER QUEUES, BULK-SERVICE, DISCRETE-TIME QUEUE, MULTIPLE VACATIONS, WAITING TIME, FACTORIZATION, SINGLE, Customer delay, Moments, Tail probabilities, Batch arrivals, Batch service, Full-batch service policy
journal title
MATHEMATICAL METHODS OF OPERATIONS RESEARCH
Math. Method Oper. Res.
volume
72
issue
1
pages
1 - 23
Web of Science type
Article
Web of Science id
000281166500001
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.848 (2010)
JCR rank
98/235 (2010)
JCR quartile
2 (2010)
ISSN
1432-2994
DOI
10.1007/s00186-009-0297-2
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
838475
handle
http://hdl.handle.net/1854/LU-838475
date created
2010-01-26 09:15:40
date last changed
2011-07-14 11:02:46
@article{838475,
  abstract     = {Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation-i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay.},
  author       = {Claeys, Dieter and Laevens, Koenraad and Walraevens, Joris and Bruneel, Herwig},
  issn         = {1432-2994},
  journal      = {MATHEMATICAL METHODS OF OPERATIONS RESEARCH},
  keyword      = {PERFORMANCE ANALYSIS,MULTISERVER QUEUES,BULK-SERVICE,DISCRETE-TIME QUEUE,MULTIPLE VACATIONS,WAITING TIME,FACTORIZATION,SINGLE,Customer delay,Moments,Tail probabilities,Batch arrivals,Batch service,Full-batch service policy},
  language     = {eng},
  number       = {1},
  pages        = {1--23},
  title        = {Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service},
  url          = {http://dx.doi.org/10.1007/s00186-009-0297-2},
  volume       = {72},
  year         = {2010},
}

Chicago
Claeys, Dieter, Koenraad Laevens, Joris Walraevens, and Herwig Bruneel. 2010. “Complete Characterisation of the Customer Delay in a Queueing System with Batch Arrivals and Batch Service.” Mathematical Methods of Operations Research 72 (1): 1–23.
APA
Claeys, Dieter, Laevens, K., Walraevens, J., & Bruneel, H. (2010). Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 72(1), 1–23.
Vancouver
1.
Claeys D, Laevens K, Walraevens J, Bruneel H. Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service. MATHEMATICAL METHODS OF OPERATIONS RESEARCH. 2010;72(1):1–23.
MLA
Claeys, Dieter, Koenraad Laevens, Joris Walraevens, et al. “Complete Characterisation of the Customer Delay in a Queueing System with Batch Arrivals and Batch Service.” MATHEMATICAL METHODS OF OPERATIONS RESEARCH 72.1 (2010): 1–23. Print.