Abstract—The problem Geom^X /G/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.

Index Terms—Bernoulli feedback; multiple vacation; bulk arrive; set-up times; stochastic decomposition; discrete time queue

Songfang Jia is with the College of Mathematics and Stastics, Chongqing, Three Gorges University, Wanzhou, Chongqing, China (corresponding author to provide phone: 023-5810-2361; fax:023-5810-2361; e-mail: jiasongfang@163.com).
Yanheng Chen is with the College of Mathematics and Stastics,Chongq-Ing Three Gorges University, Wanzhou, Chongqing, China (e-mail: math_yan@126.com).
Jinkui Liu is with the College of Mathematics and Stastics, Chongq-Ing Three Gorges University, Wanzhou, Chongqing, China (e-mail: liujinkui2006@126.com).

Cite:Songfang Jia, Yanheng Chen, and Jinkui Liu, "Steady-state Analysis of Bernoulli Feedback on Geom^X /G/1 Queue with Multiple Vacation and Set-up Times," International Journal of Applied Physics and Mathematics vol. 1, no. 1, pp. 60-65, 2011.