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A batch-service queueing model with a discrete batch Markovian arrival process

Dieter Claeys UGent, Joris Walraevens UGent, Koenraad Laevens UGent, Bart Steyaert UGent and Herwig Bruneel UGent (2010) LECTURE NOTES IN COMPUTER SCIENCE. 6148. p.1-13
abstract
Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
performance modelling, queueing systems and networks, BULK-SERVICE, PERFORMANCE ANALYSIS, MULTIPLE VACATIONS, TIME QUEUE, SINGLE, BEHAVIOR, BUFFERS
in
LECTURE NOTES IN COMPUTER SCIENCE
Lect. Notes Comput. Sci.
editor
K Al Begain, D Fiems and WJ Knottenbelt
volume
6148
issue title
ANALYTICAL AND STOCHASTIC MODELING TECHNIQUES AND APPLICATIONS, PROCEEDINGS
pages
1 - 13
publisher
Springer
place of publication
Berlin, Germany
conference name
17th International Conference on Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2010)
conference location
Cardiff, Wales, UK
conference start
2010-06-14
conference end
2010-06-16
Web of Science type
Proceedings Paper
Web of Science id
000279619100001
ISSN
0302-9743
ISBN
9783642135675
DOI
10.1007/978-3-642-13568-2_1
language
English
UGent publication?
yes
classification
P1
copyright statement
I have transferred the copyright for this publication to the publisher
id
981647
handle
http://hdl.handle.net/1854/LU-981647
date created
2010-06-21 08:51:19
date last changed
2010-07-30 13:27:23
@inproceedings{981647,
  abstract     = {Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model.},
  author       = {Claeys, Dieter and Walraevens, Joris and Laevens, Koenraad and Steyaert, Bart and Bruneel, Herwig},
  booktitle    = {LECTURE NOTES IN COMPUTER SCIENCE},
  editor       = {Al Begain, K and Fiems, D and Knottenbelt, WJ},
  isbn         = {9783642135675},
  issn         = {0302-9743},
  keyword      = {performance modelling,queueing systems and networks,BULK-SERVICE,PERFORMANCE ANALYSIS,MULTIPLE VACATIONS,TIME QUEUE,SINGLE,BEHAVIOR,BUFFERS},
  language     = {eng},
  location     = {Cardiff, Wales, UK},
  pages        = {1--13},
  publisher    = {Springer},
  title        = {A batch-service queueing model with a discrete batch Markovian arrival process},
  url          = {http://dx.doi.org/10.1007/978-3-642-13568-2\_1},
  volume       = {6148},
  year         = {2010},
}

Chicago
Claeys, Dieter, Joris Walraevens, Koenraad Laevens, Bart Steyaert, and Herwig Bruneel. 2010. “A Batch-service Queueing Model with a Discrete Batch Markovian Arrival Process.” In Lecture Notes in Computer Science, ed. K Al Begain, D Fiems, and WJ Knottenbelt, 6148:1–13. Berlin, Germany: Springer.
APA
Claeys, Dieter, Walraevens, J., Laevens, K., Steyaert, B., & Bruneel, H. (2010). A batch-service queueing model with a discrete batch Markovian arrival process. In K Al Begain, D. Fiems, & W. Knottenbelt (Eds.), LECTURE NOTES IN COMPUTER SCIENCE (Vol. 6148, pp. 1–13). Presented at the 17th International Conference on Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2010), Berlin, Germany: Springer.
Vancouver
1.
Claeys D, Walraevens J, Laevens K, Steyaert B, Bruneel H. A batch-service queueing model with a discrete batch Markovian arrival process. In: Al Begain K, Fiems D, Knottenbelt W, editors. LECTURE NOTES IN COMPUTER SCIENCE. Berlin, Germany: Springer; 2010. p. 1–13.
MLA
Claeys, Dieter, Joris Walraevens, Koenraad Laevens, et al. “A Batch-service Queueing Model with a Discrete Batch Markovian Arrival Process.” Lecture Notes in Computer Science. Ed. K Al Begain, D Fiems, & WJ Knottenbelt. Vol. 6148. Berlin, Germany: Springer, 2010. 1–13. Print.