具有不同到达率的带有启动时间的多级适应性休假Mξ/G/1排队模型

摘要

In this paper, we discuss the queue Mξ/G/1 with different arrival rates on the multiple adaptive vacations and setup times. We derive the probability generating function (p.g.f.)of the steady-state queue length by the method of embedded Markov chain and the Laplace-Stieltjes transform (LST)of the steady-state waiting time (FCFS). From the results, we obtain the conclusion that the steady-state queue length and waiting time have the property of stochastic decomposition. And we also get the LST of busy period and give several special cases. Many discussed models as to Mξ/G/1 are special cases of the model.%本文研究具有不同到达率的带有启动时间的多级适应性休假Mξ/G/1排队模型,应用嵌入马尔可夫链方法推导出了稳态队长和等待时间(先到先服务规则)分布,并验证了稳态队长和稳态等待时间具有随机分解性,而且给出了忙期分布.许多关于Mξ/G/1的排队模型都可以看作是此模型的特例.