有Bernoulli休假和可选服务的M/G/1重试反馈排队模型

考虑具有可选服务的M/G/1重试反馈排队模型,其中服务台有Bernoulli休假策略.系统外新到达的顾客服从参数为λ的泊松过程.重试区域只允许队首顾客重试,重试时间服从一般分布.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.每个顾客每次被服务完成后可以离开系统或者返回到重试区域.服务台完成一次服务以后,可以休假也可以继续为顾客服务.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.我们还得到了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.并证出在系统中服务员休假和服务台空闲的时间定义为广义休假情况下也具有随机分解特征.

An M/G/1 Retrial Queue with Feedback, Second Optional Service and Bernoulli Vacation

An M/G/1 retrial queue with feedback,second optional service and Bernoulli vacation schedules 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.Just after completion of his service,a coustomer may leave the system or may opt to repeat his service,in which case this customer rejoins the orbit queue.Further,just after completion of a customer′s service the server may take a vacation of random length or may opt to continue staying in the system to serve the next customer.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 vacation time is defined as generalized vacation.