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System occupancy in a multiclass batch-service queueing system with limited variable service capacity

Jens Baetens (UGent) , Bart Steyaert (UGent) , Dieter Claeys (UGent) and Herwig Bruneel (UGent)
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Abstract
In multi-class telecommunications or manufacturing systems, customers belonging to the same class can often be processed together. This results in a service capacity that depends on the classes of the customers in the queue. In this paper, we analyse a discrete-time batch- service queue with two customer classes. The single batch server can group all same-class customers at the head of the queue up to a constant class-dependent maximum service capac- ity. We focus on the analysis of the system occupancy at service initiation opportunities, and also compute both a light- and heavy traffic approximation in order to reduce the numeri- cal complexity introduced by the maximum service capacities. Additionally, we propose a method for interpolating between these approximations in order to study the behaviour in the intermediate region. We also deduce the system occupancy and its approximations at random slot boundaries. In the numerical experiments, we examine the conditions under which these proposed approximations are accurate.
Keywords
Management Science and Operations Research, General Decision Sciences, Batch service, Two-class, Variable service capacity, Generally distributed service times, Correlated customer types

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Please use this url to cite or link to this publication:

MLA
Baetens, Jens, et al. “System Occupancy in a Multiclass Batch-Service Queueing System with Limited Variable Service Capacity.” ANNALS OF OPERATIONS RESEARCH, 2020.
APA
Baetens, J., Steyaert, B., Claeys, D., & Bruneel, H. (2020). System occupancy in a multiclass batch-service queueing system with limited variable service capacity. ANNALS OF OPERATIONS RESEARCH.
Chicago author-date
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2020. “System Occupancy in a Multiclass Batch-Service Queueing System with Limited Variable Service Capacity.” ANNALS OF OPERATIONS RESEARCH.
Chicago author-date (all authors)
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2020. “System Occupancy in a Multiclass Batch-Service Queueing System with Limited Variable Service Capacity.” ANNALS OF OPERATIONS RESEARCH.
Vancouver
1.
Baetens J, Steyaert B, Claeys D, Bruneel H. System occupancy in a multiclass batch-service queueing system with limited variable service capacity. ANNALS OF OPERATIONS RESEARCH. 2020;
IEEE
[1]
J. Baetens, B. Steyaert, D. Claeys, and H. Bruneel, “System occupancy in a multiclass batch-service queueing system with limited variable service capacity,” ANNALS OF OPERATIONS RESEARCH, 2020.
@article{8635569,
  abstract     = {In multi-class telecommunications or manufacturing systems, customers belonging to the
same class can often be processed together. This results in a service capacity that depends
on the classes of the customers in the queue. In this paper, we analyse a discrete-time batch-
service queue with two customer classes. The single batch server can group all same-class
customers at the head of the queue up to a constant class-dependent maximum service capac-
ity. We focus on the analysis of the system occupancy at service initiation opportunities, and
also compute both a light- and heavy traffic approximation in order to reduce the numeri-
cal complexity introduced by the maximum service capacities. Additionally, we propose a
method for interpolating between these approximations in order to study the behaviour in the
intermediate region. We also deduce the system occupancy and its approximations at random
slot boundaries. In the numerical experiments, we examine the conditions under which these
proposed approximations are accurate.},
  author       = {Baetens, Jens and Steyaert, Bart and Claeys, Dieter and Bruneel, Herwig},
  issn         = {0254-5330},
  journal      = {ANNALS OF OPERATIONS RESEARCH},
  keywords     = {Management Science and Operations Research,General Decision Sciences,Batch service,Two-class,Variable service capacity,Generally distributed service times,Correlated customer types},
  language     = {eng},
  title        = {System occupancy in a multiclass batch-service queueing system with limited variable service capacity},
  url          = {http://dx.doi.org/10.1007/s10479-019-03470-1},
  year         = {2020},
}

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