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Analysis of a discrete-time queue with geometrically distributed service capacities

Herwig Bruneel UGent, Joris Walraevens UGent, Dieter Claeys UGent and Sabine Wittevrongel UGent (2012) LECTURE NOTES IN COMPUTER SCIENCE. 7314. p.121-135
abstract
We consider a discrete-time queueing model whereby the service capacity of the system, i.e., the number of work units that the system can perform per time slot, is variable from slot to slot. Specifically, we study the case where service capacities are independent from slot to slot and geometrically distributed. New customers enter the system according to a general independent arrival process. Service demands of the customers are i.i.d. and arbitrarily distributed. For this (non-classical) queueing model, we obtain explicit expressions for the probability generating functions (pgf's) of the unfinished work in the system and the queueing delay of an arbitrary customer. In case of geometric service demands, we also obtain the pgf of the number of customers in the system explicitly. By means of some numerical examples, we discuss the impact of the service process of the customers on the system behavior.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
Analytic study, Variable service capacity, Discrete-time queueing model, Closed-form results
in
LECTURE NOTES IN COMPUTER SCIENCE
Lect. Notes Comput. Sci.
editor
Khalid Al-Begain, Simonetta Balsamo and Dieter Fiems
volume
7314
issue title
Analytic and Stochastic Modeling Techniques and Applications
pages
121 - 135
publisher
Springer-Verlag
place of publication
Berlin, Germany
conference name
19th international conference on Analytical and stochastic modeling techniques and applications (ASMTA-2012)
conference location
Grenoble, France
conference start
2012-06-02
conference end
2012-06-04
ISSN
0302-9743
ISBN
9783642307812
DOI
10.1007/978-3-642-30782-9_9
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
VABB id
c:vabb:339811
VABB type
VABB-5
id
2138180
handle
http://hdl.handle.net/1854/LU-2138180
date created
2012-06-11 10:12:16
date last changed
2012-06-13 13:06:09
@inproceedings{2138180,
  abstract     = {We consider a discrete-time queueing model whereby the service capacity of the system, i.e., the number of work units that the system can perform per time slot, is variable from slot to slot. Specifically, we study the case where service capacities are independent from slot to slot and geometrically distributed. New customers enter the system according to a general independent arrival process. Service demands of the customers are i.i.d. and arbitrarily distributed. For this (non-classical) queueing model, we obtain explicit expressions for the probability generating functions (pgf's) of the unfinished work in the system and the queueing delay of an arbitrary customer. In case of geometric service demands, we also obtain the pgf of the number of customers in the system explicitly. By means of some numerical examples, we discuss the impact of the service process of the customers on the system behavior.},
  author       = {Bruneel, Herwig and Walraevens, Joris and Claeys, Dieter and Wittevrongel, Sabine},
  booktitle    = {LECTURE NOTES IN COMPUTER SCIENCE},
  editor       = {Al-Begain, Khalid  and Balsamo, Simonetta  and Fiems, Dieter },
  isbn         = {9783642307812},
  issn         = {0302-9743},
  keyword      = {Analytic study,Variable service capacity,Discrete-time queueing model,Closed-form results},
  language     = {eng},
  location     = {Grenoble, France},
  pages        = {121--135},
  publisher    = {Springer-Verlag},
  title        = {Analysis of a discrete-time queue with geometrically distributed service capacities},
  url          = {http://dx.doi.org/10.1007/978-3-642-30782-9\_9},
  volume       = {7314},
  year         = {2012},
}

Chicago
Bruneel, Herwig, Joris Walraevens, Dieter Claeys, and Sabine Wittevrongel. 2012. “Analysis of a Discrete-time Queue with Geometrically Distributed Service Capacities.” In Lecture Notes in Computer Science, ed. Khalid Al-Begain, Simonetta Balsamo, and Dieter Fiems, 7314:121–135. Berlin, Germany: Springer-Verlag.
APA
Bruneel, H., Walraevens, J., Claeys, D., & Wittevrongel, S. (2012). Analysis of a discrete-time queue with geometrically distributed service capacities. In Khalid Al-Begain, S. Balsamo, & D. Fiems (Eds.), LECTURE NOTES IN COMPUTER SCIENCE (Vol. 7314, pp. 121–135). Presented at the 19th international conference on Analytical and stochastic modeling techniques and applications (ASMTA-2012), Berlin, Germany: Springer-Verlag.
Vancouver
1.
Bruneel H, Walraevens J, Claeys D, Wittevrongel S. Analysis of a discrete-time queue with geometrically distributed service capacities. In: Al-Begain K, Balsamo S, Fiems D, editors. LECTURE NOTES IN COMPUTER SCIENCE. Berlin, Germany: Springer-Verlag; 2012. p. 121–35.
MLA
Bruneel, Herwig, Joris Walraevens, Dieter Claeys, et al. “Analysis of a Discrete-time Queue with Geometrically Distributed Service Capacities.” Lecture Notes in Computer Science. Ed. Khalid Al-Begain, Simonetta Balsamo, & Dieter Fiems. Vol. 7314. Berlin, Germany: Springer-Verlag, 2012. 121–135. Print.