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A multi-class discrete-time queueing system under the FCFS service discipline

Sofian De Clercq UGent, Koenraad Laevens UGent, Bart Steyaert UGent and Herwig Bruneel UGent (2013) ANNALS OF OPERATIONS RESEARCH. 202(1). p.59-73
abstract
The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn’t actually determine 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 quantities such as queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a multi-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 random order. It will be our goal to search for the steady-state distribution of queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the random order of service is equivalent to FCFS if different customers have different arrival epochs within this time-slot and if the arrival epochs are independent of customer class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a slot as a bounded continuous time frame.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Random order, Generating function, FCFS, Queueing theory, BUFFER, PERFORMANCE, PRIORITY, ARRIVAL STREAMS, LENGTH DISTRIBUTION, SINGLE-SERVER QUEUE
journal title
ANNALS OF OPERATIONS RESEARCH
Ann. Oper. Res.
volume
202
issue
1
pages
59 - 73
Web of Science type
Article
Web of Science id
000312713200005
JCR category
OPERATIONS RESEARCH & MANAGEMENT SCIENCE
JCR impact factor
1.103 (2013)
JCR rank
35/79 (2013)
JCR quartile
2 (2013)
ISSN
0254-5330
DOI
10.1007/s10479-011-1051-8
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2913844
handle
http://hdl.handle.net/1854/LU-2913844
date created
2012-06-20 17:48:23
date last changed
2013-02-08 15:36:31
@article{2913844,
  abstract     = {The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn{\textquoteright}t actually determine what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into {\textquoteleft}during the same time-slot{\textquoteright}. In other words, it doesn{\textquoteright}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 quantities such as queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a multi-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 random order. It will be our goal to search for the steady-state distribution of queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the random order of service is equivalent to FCFS if different customers have different arrival epochs within this time-slot and if the arrival epochs are independent of customer class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a slot as a bounded continuous time frame.},
  author       = {De Clercq, Sofian and Laevens, Koenraad and Steyaert, Bart and Bruneel, Herwig},
  issn         = {0254-5330},
  journal      = {ANNALS OF OPERATIONS RESEARCH},
  keyword      = {Random order,Generating function,FCFS,Queueing theory,BUFFER,PERFORMANCE,PRIORITY,ARRIVAL STREAMS,LENGTH DISTRIBUTION,SINGLE-SERVER QUEUE},
  language     = {eng},
  number       = {1},
  pages        = {59--73},
  title        = {A multi-class discrete-time queueing system under the FCFS service discipline},
  url          = {http://dx.doi.org/10.1007/s10479-011-1051-8},
  volume       = {202},
  year         = {2013},
}

Chicago
De Clercq, Sofian, Koenraad Laevens, Bart Steyaert, and Herwig Bruneel. 2013. “A Multi-class Discrete-time Queueing System Under the FCFS Service Discipline.” Annals of Operations Research 202 (1): 59–73.
APA
De Clercq, Sofian, Laevens, K., Steyaert, B., & Bruneel, H. (2013). A multi-class discrete-time queueing system under the FCFS service discipline. ANNALS OF OPERATIONS RESEARCH, 202(1), 59–73.
Vancouver
1.
De Clercq S, Laevens K, Steyaert B, Bruneel H. A multi-class discrete-time queueing system under the FCFS service discipline. ANNALS OF OPERATIONS RESEARCH. 2013;202(1):59–73.
MLA
De Clercq, Sofian, Koenraad Laevens, Bart Steyaert, et al. “A Multi-class Discrete-time Queueing System Under the FCFS Service Discipline.” ANNALS OF OPERATIONS RESEARCH 202.1 (2013): 59–73. Print.