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Single server retrial queues with speed scaling: analysis and performance evaluation

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Abstract
Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we first study a basic case and then subsequently incorporate the concepts of a setup time and a deactivation time in extended versions of the model. In all cases, we obtain a full characterization of the stationary queue length distribution. This allows us to evaluate the performance in terms of the mentioned balance between performance and energy, using an existing cost function as well as a newly proposed variant thereof. This paper presents the derivation of the stationary distribution as well as several numerical examples of the cost-based performance evaluation.
Keywords
CONSUMPTION, TIME, Data center, energy efficiency, speed scaling, setup time, deactivation, time, retrial queue

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Citation

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

MLA
Tuan Phung-Duc, Tuan Phung-Duc, Wouter Rogiest, and Sabine Wittevrongel. “Single Server Retrial Queues with Speed Scaling: Analysis and Performance Evaluation.” JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 13.4 (2017): 1927–1943. Print.
APA
Tuan Phung-Duc, T. P.-D., Rogiest, W., & Wittevrongel, S. (2017). Single server retrial queues with speed scaling: analysis and performance evaluation. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 13(4), 1927–1943.
Chicago author-date
Tuan Phung-Duc, Tuan Phung-Duc, Wouter Rogiest, and Sabine Wittevrongel. 2017. “Single Server Retrial Queues with Speed Scaling: Analysis and Performance Evaluation.” Journal of Industrial and Management Optimization 13 (4): 1927–1943.
Chicago author-date (all authors)
Tuan Phung-Duc, Tuan Phung-Duc, Wouter Rogiest, and Sabine Wittevrongel. 2017. “Single Server Retrial Queues with Speed Scaling: Analysis and Performance Evaluation.” Journal of Industrial and Management Optimization 13 (4): 1927–1943.
Vancouver
1.
Tuan Phung-Duc TP-D, Rogiest W, Wittevrongel S. Single server retrial queues with speed scaling: analysis and performance evaluation. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION. Springfield: Amer Inst Mathematical Sciences-aims; 2017;13(4):1927–43.
IEEE
[1]
T. P.-D. Tuan Phung-Duc, W. Rogiest, and S. Wittevrongel, “Single server retrial queues with speed scaling: analysis and performance evaluation,” JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, vol. 13, no. 4, pp. 1927–1943, 2017.
@article{8538263,
  abstract     = {Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we first study a basic case and then subsequently incorporate the concepts of a setup time and a deactivation time in extended versions of the model. In all cases, we obtain a full characterization of the stationary queue length distribution. This allows us to evaluate the performance in terms of the mentioned balance between performance and energy, using an existing cost function as well as a newly proposed variant thereof. This paper presents the derivation of the stationary distribution as well as several numerical examples of the cost-based performance evaluation.},
  author       = {Tuan Phung-Duc, Tuan Phung-Duc and Rogiest, Wouter and Wittevrongel, Sabine},
  issn         = {1547-5816},
  journal      = {JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION},
  keywords     = {CONSUMPTION,TIME,Data center,energy efficiency,speed scaling,setup time,deactivation,time,retrial queue},
  language     = {eng},
  number       = {4},
  pages        = {1927--1943},
  publisher    = {Amer Inst Mathematical Sciences-aims},
  title        = {Single server retrial queues with speed scaling: analysis and performance evaluation},
  url          = {http://dx.doi.org/10.3934/jimo.2017025},
  volume       = {13},
  year         = {2017},
}

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