具有不同到达率的带有启动时间及不耐烦策略的多级适应性休假M^X/G/1排队

Queue M^x/G/1 with impatient policy,different arrival rates,multiple adaptive vacations and setup times

研究了具有不同到达率的带有启动时间及不耐烦策略的多级适应性休假MX/G/1排队模型,通过嵌入马尔可夫链方法推导出稳态队长的母函数、等待时间的LST(先到先服务规则),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、全忙期及在线期均值。

A continuous time queue M^x/G/1 with impatient policy, different arrival rates, multiple vacations and setup times is considered. The generating function of the steady state queue length is derived by the method of the em- bedded Markov chain and the Laplace-Stieltjes transform （LST） of the steady-state waiting time （FCFS）. From the results it is concluded that the steady-state queue length and the waiting time have the property of the stochastic decomposition. The mean of the busy period, the whole vacation and the on-line period are also obtained.