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Influence of correlation in the arrival process on batch-service queueing systems

Dieter Claeys (UGent) , Bart Steyaert (UGent) , Joris Walraevens (UGent) , Koenraad Laevens (UGent) and Herwig Bruneel (UGent)
Author
Organization
Abstract
Numerous studies demonstrate that correlation in the arrival process might have a significant influence on the behaviour of queueing systems. The impact of correlation on batch-service queueing systems, nevertheless, has attracted nearly no attention, and therefore constitutes the subject of this contribution. More specifically, we deduce various performance measures related to the buffer content in a system whereby the batch server only initiates service if the buffer content reaches or exceeds some server threshold. Such a threshold leads to a better utilization of the server capacity. We further include a general dependency between the service time of a batch and the number of customers within it. In addition, we model the correlation by a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. This process is the subject of many papers, as it has the advantage that it can capture most arrival patterns up to any desired precision. By means of the obtained performance measures, we examine the influence of correlation on the behaviour of the system. For instance, we demonstrate that disregarding correlation, although it might lead to a severe underestimation of the buffer content, has only a small influence on the value of the optimal server threshold.

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Chicago
Claeys, Dieter, Bart Steyaert, Joris Walraevens, Koenraad Laevens, and Herwig Bruneel. 2010. “Influence of Correlation in the Arrival Process on Batch-service Queueing Systems.” In Queueing Theory, 3rd Madrid Conference, Booklet of Abstracts, 29–29.
APA
Claeys, Dieter, Steyaert, B., Walraevens, J., Laevens, K., & Bruneel, H. (2010). Influence of correlation in the arrival process on batch-service queueing systems. Queueing Theory, 3rd Madrid conference, Booklet of abstracts (pp. 29–29). Presented at the 3rd Madrid conference on Queueing Theory (MCQT  ’10).
Vancouver
1.
Claeys D, Steyaert B, Walraevens J, Laevens K, Bruneel H. Influence of correlation in the arrival process on batch-service queueing systems. Queueing Theory, 3rd Madrid conference, Booklet of abstracts. 2010. p. 29–29.
MLA
Claeys, Dieter, Bart Steyaert, Joris Walraevens, et al. “Influence of Correlation in the Arrival Process on Batch-service Queueing Systems.” Queueing Theory, 3rd Madrid Conference, Booklet of Abstracts. 2010. 29–29. Print.
@inproceedings{1041812,
  abstract     = {Numerous studies demonstrate that correlation in the arrival process might have a significant influence on the behaviour of queueing systems. The impact of correlation on batch-service queueing systems, nevertheless, has attracted nearly no attention, and therefore constitutes the subject of this contribution. More specifically, we deduce various performance measures related to the buffer content in a system whereby the batch server only initiates service if the buffer content reaches or exceeds some server threshold. Such a threshold leads to a better utilization of the server capacity. We further include a general dependency between the service time of a batch and the number of customers within it. In addition, we model the correlation by a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. This process is the subject of many papers, as it has the advantage that it can capture most arrival patterns up to any desired precision. 
By means of the obtained performance measures, we examine the influence of correlation on the behaviour of the system. For instance, we demonstrate that disregarding correlation, although it might lead to a severe underestimation of the buffer content, has only a small influence on the value of the optimal server threshold.},
  author       = {Claeys, Dieter and Steyaert, Bart and Walraevens, Joris and Laevens, Koenraad and Bruneel, Herwig},
  booktitle    = {Queueing Theory, 3rd Madrid conference, Booklet of abstracts},
  language     = {eng},
  location     = {Toledo, Spain},
  pages        = {29--29},
  title        = {Influence of correlation in the arrival process on batch-service queueing systems},
  year         = {2010},
}