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FCFS in dual-class discrete-time queueing systems

Sofian De Clercq UGent, Koenraad Laevens, Bart Steyaert UGent and Herwig Bruneel UGent (2010) Queueing Theory, 3rd Madrid conference, Booklet of abstracts. p.30-30
abstract
The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn't actually say what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into 'during the same time-slot'. In other words, it doesn't specify in which order such customers are served? When we consider multiple types of customers, each requiring different service time distributions, the precise order of service even starts to affect things like queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a dual-class discrete-time queueing system with a general independent arrival process and generally distributed service times. The service discipline is FCFS and customers entering during the same time-slot are served in an arbitrary order. It will be our goal to search for queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the arbitrary service order is equivalent to FCFS if different customers have different arrival epochs and if the arrival epochs are independent of class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a bounded continuous time frame. The equivalent problem in continuous time has thus far only been solved for a Poissonian arrival process, and some specific cases of MAP.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
in
Queueing Theory, 3rd Madrid conference, Booklet of abstracts
pages
30 - 30
conference name
3rd Madrid conference on Queueing Theory (MCQT '10)
conference location
Toledo, Spain
conference start
2010-06-28
conference end
2010-07-01
language
English
UGent publication?
yes
classification
C3
copyright statement
I have transferred the copyright for this publication to the publisher
id
1177047
handle
http://hdl.handle.net/1854/LU-1177047
date created
2011-02-28 17:30:20
date last changed
2016-12-19 15:35:09
@inproceedings{1177047,
  abstract     = {The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn't actually say what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into 'during the same time-slot'. In other words, it doesn't specify in which order such customers are served? When we consider multiple types of customers, each requiring different service time distributions, the precise order of service even starts to affect things like queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a dual-class discrete-time queueing system with a general independent arrival process and generally distributed service times. The service discipline is FCFS and customers entering during the same time-slot are served in an arbitrary order. It will be our goal to search for queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the arbitrary service order is equivalent to FCFS if different customers have different arrival epochs and if the arrival epochs are independent of class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a bounded continuous time frame. The equivalent problem in continuous time has thus far only been solved for a Poissonian arrival process, and some specific cases of MAP.},
  author       = {De Clercq, Sofian and Laevens, Koenraad and Steyaert, Bart and Bruneel, Herwig},
  booktitle    = {Queueing Theory, 3rd Madrid conference, Booklet of abstracts},
  language     = {eng},
  location     = {Toledo, Spain},
  pages        = {30--30},
  title        = {FCFS in dual-class discrete-time queueing systems},
  year         = {2010},
}

Chicago
De Clercq, Sofian, Koenraad Laevens, Bart Steyaert, and Herwig Bruneel. 2010. “FCFS in Dual-class Discrete-time Queueing Systems.” In Queueing Theory, 3rd Madrid Conference, Booklet of Abstracts, 30–30.
APA
De Clercq, Sofian, Laevens, K., Steyaert, B., & Bruneel, H. (2010). FCFS in dual-class discrete-time queueing systems. Queueing Theory, 3rd Madrid conference, Booklet of abstracts (pp. 30–30). Presented at the 3rd Madrid conference on Queueing Theory (MCQT  ’10).
Vancouver
1.
De Clercq S, Laevens K, Steyaert B, Bruneel H. FCFS in dual-class discrete-time queueing systems. Queueing Theory, 3rd Madrid conference, Booklet of abstracts. 2010. p. 30–30.
MLA
De Clercq, Sofian, Koenraad Laevens, Bart Steyaert, et al. “FCFS in Dual-class Discrete-time Queueing Systems.” Queueing Theory, 3rd Madrid Conference, Booklet of Abstracts. 2010. 30–30. Print.