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An analysis of a batch server with variable and class-dependent service capacity

Jens Baetens (UGent) , Bart Steyaert (UGent) , Dieter Claeys (UGent) and Herwig Bruneel (UGent)
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Abstract
In many studies on batch service queueing systems, the service capacity is assumed to be constant. However, this service capacity often depends on the content of the queue. In this paper, we analyse a discrete-time single server batch server queue with general inde- pendent arrivals. We distinguish two di erent classes in the arrival stream and products of both classes are added to the tail of a single queue. The single batch server can group all waiting customers at the head of the queue that belong to the same product class up to a certain class-dependent maximum capacity. This results in a stochastic service capacity that depends on both the number of customers in the queue and their respective classes. Since it is clear that the length of a sequence of same-class customers will have a signi cant impact on the performance of the system, we also include correlation between the classes of consecutive customers. Applications of this type of batch server can, for instance, be found in the pacemaker loop of a Lean manufacturing system. In the course of the analysis, we calculate the probability generating function of the system occupancy at service initi- ation opportunities. In the numerical experiments, we will look at the impact of di erent parameters on both the mean system occupancy and the probability that the server is idle at a random service initiation opportunity. We also provide a number of guidelines to pick between the exact solution and an approximated approach with unlimited service capacities, by looking at the trade-o between accuracy and computational complexity.
Keywords
Queueing, 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. “An Analysis of a Batch Server with Variable and Class-dependent Service Capacity.” 3rd European Conference on Queueing Theory : Abstracts. 2018. Print.
APA
Baetens, Jens, Steyaert, B., Claeys, D., & Bruneel, H. (2018). An analysis of a batch server with variable and class-dependent service capacity. 3rd European Conference on Queueing Theory : abstracts. Presented at the 3rd European Conference on Queueing Theory.
Chicago author-date
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2018. “An Analysis of a Batch Server with Variable and Class-dependent Service Capacity.” In 3rd European Conference on Queueing Theory : Abstracts.
Chicago author-date (all authors)
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2018. “An Analysis of a Batch Server with Variable and Class-dependent Service Capacity.” In 3rd European Conference on Queueing Theory : Abstracts.
Vancouver
1.
Baetens J, Steyaert B, Claeys D, Bruneel H. An analysis of a batch server with variable and class-dependent service capacity. 3rd European Conference on Queueing Theory : abstracts. 2018.
IEEE
[1]
J. Baetens, B. Steyaert, D. Claeys, and H. Bruneel, “An analysis of a batch server with variable and class-dependent service capacity,” in 3rd European Conference on Queueing Theory : abstracts, Jerusalem - Israel, 2018.
@inproceedings{8575571,
  abstract     = {In many studies on batch service queueing systems, the service capacity is assumed to
be constant. However, this service capacity often depends on the content of the queue. In
this paper, we analyse a discrete-time single server batch server queue with general inde-
pendent arrivals. We distinguish two dierent classes in the arrival stream and products of
both classes are added to the tail of a single queue. The single batch server can group all
waiting customers at the head of the queue that belong to the same product class up to
a certain class-dependent maximum capacity. This results in a stochastic service capacity
that depends on both the number of customers in the queue and their respective classes.
Since it is clear that the length of a sequence of same-class customers will have a signicant
impact on the performance of the system, we also include correlation between the classes
of consecutive customers. Applications of this type of batch server can, for instance, be
found in the pacemaker loop of a Lean manufacturing system. In the course of the analysis,
we calculate the probability generating function of the system occupancy at service initi-
ation opportunities. In the numerical experiments, we will look at the impact of dierent
parameters on both the mean system occupancy and the probability that the server is idle
at a random service initiation opportunity. We also provide a number of guidelines to pick
between the exact solution and an approximated approach with unlimited service capacities,
by looking at the trade-o between accuracy and computational complexity.},
  author       = {Baetens, Jens and Steyaert, Bart and Claeys, Dieter and Bruneel, Herwig},
  booktitle    = {3rd European Conference on Queueing Theory : abstracts},
  keywords     = {Queueing,Batch Service,Two-Class,Variable Service Capacity,Generally distributed service times,Correlated customer types},
  language     = {eng},
  location     = {Jerusalem - Israel},
  pages        = {1},
  title        = {An analysis of a batch server with variable and class-dependent service capacity},
  year         = {2018},
}