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Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1

Dieter Claeys UGent, Joris Walraevens UGent, Koenraad Laevens UGent and Herwig Bruneel UGent (2010) 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH. 8(3). p.255-269
abstract
In this paper, we compute the probability generating functions (PGF's) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be obtained from these PGF's, through which we study and compare both systems. We pay special attention to the influence of the distribution of the arrival batch sizes. The main observation is that the difference between the two policies depends highly on this distribution. Another conclusion is that the results are considerably different as compared to Bernoulli (single) arrivals, which are frequently considered in the literature. This demonstrates the necessity of modeling the arrivals as batches.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
QUEUES, VACATIONS, WAITING TIME, BULK SERVICE, RULE, Batch service, Batch arrivals, Immediate versus full-batch service policy, Customer delay
journal title
4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH
4OR Q. J. Oper. Res.
volume
8
issue
3
pages
255 - 269
Web of Science type
Article
Web of Science id
000283396800003
JCR category
OPERATIONS RESEARCH & MANAGEMENT SCIENCE
JCR impact factor
0.69 (2010)
JCR rank
52/74 (2010)
JCR quartile
3 (2010)
ISSN
1619-4500
DOI
10.1007/s10288-009-0111-2
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
838327
handle
http://hdl.handle.net/1854/LU-838327
date created
2010-01-26 08:43:32
date last changed
2011-07-14 11:04:38
@article{838327,
  abstract     = {In this paper, we compute the probability generating functions (PGF's) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be obtained from these PGF's, through which we study and compare both systems. We pay special attention to the influence of the distribution of the arrival batch sizes. The main observation is that the difference between the two policies depends highly on this distribution. Another conclusion is that the results are considerably different as compared to Bernoulli (single) arrivals, which are frequently considered in the literature. This demonstrates the necessity of modeling the arrivals as batches.},
  author       = {Claeys, Dieter and Walraevens, Joris and Laevens, Koenraad and Bruneel, Herwig},
  issn         = {1619-4500},
  journal      = {4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH},
  keyword      = {QUEUES,VACATIONS,WAITING TIME,BULK SERVICE,RULE,Batch service,Batch arrivals,Immediate versus full-batch service policy,Customer delay},
  language     = {eng},
  number       = {3},
  pages        = {255--269},
  title        = {Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1},
  url          = {http://dx.doi.org/10.1007/s10288-009-0111-2},
  volume       = {8},
  year         = {2010},
}

Chicago
Claeys, Dieter, Joris Walraevens, Koenraad Laevens, and Herwig Bruneel. 2010. “Delay Analysis of Two Batch-service Queueing Models with Batch Arrivals: Geo(X)/Geo(c)/1.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 8 (3): 255–269.
APA
Claeys, Dieter, Walraevens, J., Laevens, K., & Bruneel, H. (2010). Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, 8(3), 255–269.
Vancouver
1.
Claeys D, Walraevens J, Laevens K, Bruneel H. Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH. 2010;8(3):255–69.
MLA
Claeys, Dieter, Joris Walraevens, Koenraad Laevens, et al. “Delay Analysis of Two Batch-service Queueing Models with Batch Arrivals: Geo(X)/Geo(c)/1.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 8.3 (2010): 255–269. Print.