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A decomposition result for single server discrete-time qeues with generalized vacations

Sofian De Clercq (UGent) , Bart Steyaert (UGent) and Herwig Bruneel (UGent)
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Abstract
For several specific discrete-time queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. This paper aims to show that this decomposition can be applied to for a large class of discrete-time queueing systems with vacations. The analysis builds on results obtained by Fuhrmann and Cooper concerning continuous-time queueing systems with Poissonian arrivals. Through some examples we show that the queueing analysis can be considerably simplified using this decomposition property.
Keywords
Queueing Theory, Generating Function, Stochastic Decomposition

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Chicago
De Clercq, Sofian, Bart Steyaert, and Herwig Bruneel. 2011. “A Decomposition Result for Single Server Discrete-time Qeues with Generalized Vacations.” In 6th International Conference on Queueing Theory and Network Applications, Proceedings, ed. Bara Kim, Ho Woo Lee, Gang Uk Hwang, and Yang Woo Shin, 38–43. ACM.
APA
De Clercq, Sofian, Steyaert, B., & Bruneel, H. (2011). A decomposition result for single server discrete-time qeues with generalized vacations. In B. Kim, H. W. Lee, G. U. Hwang, & Y. W. Shin (Eds.), 6th international conference on Queueing Theory and Network Applications, Proceedings (pp. 38–43). Presented at the 6th International Conference on Queueing Theory and Network Applications (QTNA - 2011), ACM.
Vancouver
1.
De Clercq S, Steyaert B, Bruneel H. A decomposition result for single server discrete-time qeues with generalized vacations. In: Kim B, Lee HW, Hwang GU, Shin YW, editors. 6th international conference on Queueing Theory and Network Applications, Proceedings. ACM; 2011. p. 38–43.
MLA
De Clercq, Sofian, Bart Steyaert, and Herwig Bruneel. “A Decomposition Result for Single Server Discrete-time Qeues with Generalized Vacations.” 6th International Conference on Queueing Theory and Network Applications, Proceedings. Ed. Bara Kim et al. ACM, 2011. 38–43. Print.
@inproceedings{1894545,
  abstract     = {For several specific discrete-time queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. This paper aims to show that this decomposition can be applied to for a large class of discrete-time queueing systems with vacations. The analysis builds on results obtained by Fuhrmann and Cooper concerning continuous-time queueing systems with Poissonian arrivals. Through some examples we show that the queueing analysis can be considerably simplified using this decomposition property.},
  author       = {De Clercq, Sofian and Steyaert, Bart and Bruneel, Herwig},
  booktitle    = {6th international conference on Queueing Theory and Network Applications, Proceedings},
  editor       = {Kim, Bara and Lee, Ho Woo and Hwang, Gang Uk and Shin, Yang Woo},
  isbn         = {9781450307581},
  keyword      = {Queueing Theory,Generating Function,Stochastic Decomposition},
  language     = {eng},
  location     = {Seoul, South Korea},
  pages        = {38--43},
  publisher    = {ACM},
  title        = {A decomposition result for single server discrete-time qeues with generalized vacations},
  year         = {2011},
}