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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
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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.
Keywords
Random order, Generating function, FCFS, Queueing theory, BUFFER, PERFORMANCE, PRIORITY, ARRIVAL STREAMS, LENGTH DISTRIBUTION, SINGLE-SERVER QUEUE

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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.
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.
Chicago author-date
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.
Chicago author-date (all authors)
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.
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.
IEEE
[1]
S. De Clercq, K. Laevens, B. Steyaert, and H. Bruneel, “A multi-class discrete-time queueing system under the FCFS service discipline,” ANNALS OF OPERATIONS RESEARCH, vol. 202, no. 1, pp. 59–73, 2013.
@article{2913844,
  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.}},
  author       = {{De Clercq, Sofian and Laevens, Koenraad and Steyaert, Bart and Bruneel, Herwig}},
  issn         = {{0254-5330}},
  journal      = {{ANNALS OF OPERATIONS RESEARCH}},
  keywords     = {{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}},
}

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