Discrete-time Geo(X)/G/1 queue with unreliable server and multiple adaptive delayed vacations

作者：Tang, Yinghui^*; Yun, Xi; Huang, Shujuan

来源：Journal of Computational and Applied Mathematics, 2008, 220(1-2): 439-455.

DOI：10.1016/j.cam.2007.08.019

• discrete-time queueing model
• multiple adaptive delayed vacation
• unreliable
• transient and steady-state distributions
• stochastic decomposition

In this paper we consider a discrete-time Geo(X)/G/1 queue with unreliable server and multiple adaptive delayed vacations policy in which the vacation time, service time, repair time and the delayed time all follow arbitrary discrete distribution. By using a concise decomposition method, the transient and steady-state distributions of the queue length are studied, and the stochastic decomposition property of steady-state queue length has been proved. Several common vacation policies are special cases of the vacation policy presented in this study. The relationship between the generating functions of steady-state queue length at departure epoch and arbitrary epoch is obtained. Finally, we give some numerical examples to illustrate the effect of the parameters on several performance characteristics.

• 出版日期2008-10-15
• 单位电子科技大学; 四川师范大学