中文摘要：

离散时间排队比连续时间排队在有时间间隔的系统中更适合建立模型，例如计算机和通讯系统。考虑一个具有二次可选休假和一般重试时间的Geo/G/1离散重试排队模型。采用补充变量法和构造母函数等方法研究该系统在稳态条件下轨道顾客数、系统顾客数的概率母函数和随机分解等性质，通过模型的特例来验证模型的正确性。最后给出一些数值例子分析不同的参数对系统性能指标的影响。

英文摘要：

Discrete time queues are more appropriate to modeling slotted systems than continuous time queues,such as computer and communication systems. In this paper,a discrete-time Geo/G/1 retrial queue with second optional vacation where the retrial times follow a general distribution was studied. The probability generating functions of the orbit size,system size and stochastic decomposition property in steady-state were studied using supplementary variable technique and probability generating functions method. In addition, this model is verified by special examples. Finally, numerical examples are presented to illustrate the effects of different parameters on the system performances.