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System occupancy of a two-class batch-service queue with class-dependent variable server capacity

Jens Baetens (UGent) , Bart Steyaert (UGent) , Dieter Claeys (UGent) and Herwig Bruneel (UGent)
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Abstract
Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common first-come-first served single-server queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the number of consecutive same-class customers. After establishing the system equations that govern the system behaviour, we deduce an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. Also, some numerical examples are given that provide further insight in the impact of the different parameters on the system performance.
Keywords
Batch Service, Discrete Time, Two Classes, Queueing, Variable Server Capacity

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

Chicago
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2016. “System Occupancy of a Two-class Batch-service Queue with Class-dependent Variable Server Capacity.” In Analytical and Stochastic Modelling Techniques and Applications , 9845:32–44. Springer.
APA
Baetens, Jens, Steyaert, B., Claeys, D., & Bruneel, H. (2016). System occupancy of a two-class batch-service queue with class-dependent variable server capacity. Analytical and Stochastic Modelling Techniques and Applications (Vol. 9845, pp. 32–44). Presented at the 23rd International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA) , Springer.
Vancouver
1.
Baetens J, Steyaert B, Claeys D, Bruneel H. System occupancy of a two-class batch-service queue with class-dependent variable server capacity. Analytical and Stochastic Modelling Techniques and Applications . Springer; 2016. p. 32–44.
MLA
Baetens, Jens, Bart Steyaert, Dieter Claeys, et al. “System Occupancy of a Two-class Batch-service Queue with Class-dependent Variable Server Capacity.” Analytical and Stochastic Modelling Techniques and Applications . Vol. 9845. Springer, 2016. 32–44. Print.
@inproceedings{8075277,
  abstract     = {Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common first-come-first served single-server queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the number of consecutive same-class customers. After establishing the system equations that govern the system behaviour, we deduce an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. Also, some numerical examples are given that provide further insight in the impact of the different parameters on the system performance.},
  author       = {Baetens, Jens and Steyaert, Bart and Claeys, Dieter and Bruneel, Herwig},
  booktitle    = {Analytical and Stochastic Modelling Techniques and Applications },
  isbn         = {978-3-319-43903-7},
  issn         = {1611-3349},
  keyword      = {Batch Service,Discrete Time,Two Classes,Queueing,Variable Server Capacity},
  language     = {eng},
  location     = {Cardiff, WALES },
  pages        = {32--44},
  publisher    = {Springer},
  title        = {System occupancy of a two-class batch-service queue with class-dependent variable server capacity},
  url          = {http://dx.doi.org/10.1007/978-3-319-43904-4\_3},
  volume       = {9845},
  year         = {2016},
}

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