doi: 10.7763/IJAPM.2011.V1.12
Steady-state Analysis of Bernoulli Feedback on <i>Geom<sup>X</sup> /G</i>/1 Queue with Multiple Vacation and Set-up Times
Songfang Jia
1,*
,
Yanheng Chen
2,*
,
Jinkui Liu
2
- 1 the College of Mathematics and Stastics, Chongqing, Three Gorges University, Wanzhou, Chongqing, China (corresponding author to provide
- 2 the College of Mathematics and Stastics,Chongq-Ing Three Gorges University, Wanzhou, Chongqing, China
Abstract
The problem <i>Geom<sup>X</sup> /G</i>/1, a queuing model of discrete time with Bernoulli feedback, multiple vacation and Set-up times is considered. The generating function of the steady state queue length, waiting time and their stochastic decomposition are derived. And we also get the generating function of busy period, give some special cases, and present some numerical examples to study the effect of the varying parameters on the main Perf-ormance characteristics of our system.
Keywords
- Bernoulli
- feedback;
- multiple
- vacation;
- bulk
- arrive;
- set-up
- times;
- stochastic
- decomposition;
- discrete
- time
- queue
How to Cite
Songfang Jia, Yanheng Chen, and Jinkui Liu, "Steady-state Analysis of Bernoulli Feedback on <i>Geom<sup>X</sup> /G</i>/1 Queue with Multiple Vacation and Set-up Times," International Journal of Applied Physics and Mathematics, vol. 1, no. 1, pp. 60-65, 2011. https://doi.org/ 10.7763/IJAPM.2011.V1.12
Copyright & License
Copyright © 2011 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).