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中文摘要：
考虑具有可选服务的M／G／1重试排队模型，其中服务台有可能启动失败．系统外新到达的顾客服从参数为A的泊松过程．重试区域只允许队首顾客重试，重试时间服务一般分布．所有的顾客都必须接受必选服务，然而只有其中部分接受可选服务．通过嵌入马尔可夫链法证明了系统稳态的充要条件．利用补充变量的方法得到了稳态时系统和重试区域中队长分布．我们还得到重试期间服务台处于空闲的概率，重试区域为空的概率以及其他各种指标．并证出在把系统中服务台空闲和修理的时间定义为广义休假情况下也具有随机分解特征．
英文摘要：
An M/G/1 retrial queue with second optional service and starting failures is considered. We assume that customers arrive to the system according to a Poisson process with rate λ. Assuming that only the customer at the head of the orbit has priority access to the server, and the retrial time is an arbitrary distribution. All demand the first ＂essential＂ service, whereas only some of them demand the second ＂optional＂ service. The necessary and sufficient condition for the system stability is derived through embedded Markov chain. The steady-state distributions of the number of customers in the system and orbit are obtained along with method of supplementary variables. We also derived the probability that the server is in idle when retrial, the probability that there is no one in orbit and other performance measures. A general decomposition law for this system is established on condition that the server idle time and repair time is defined as generalized vacation.
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