带启动期的M^([x])/M/1/SWV排队系统

The M^([X])/M/1/SWV queue with start-up time

针对连续时间带启动期成批到达M[x]/M/1单重工作休假排队系统,建立了模型的三维Markov链,并给出了稳态队长的母函数及其随机分解。利用条件Erlang分布的双参数加法定理,得到了Laplace变换序下的稳态等待时间的上下界以及平均队长、平均等待时间的上下界、平均逗留时间等性能指标。最后通过数值实例验证了所得出的结论。

A batch arrival M^[X]/M/1 with start-up time and single working vacations is considered. A model of a three- dimensional Markov chain is established. Then, the PGF and the stochastic decomposition of the stea-dy-state are given. The two parameters addition theorem of condition Erlang distribution are obtained, with which the upper and lower bounds of steady-state waiting time is given under Laplace transform order. The mean queue length, the mean waiting time of the upper and lower bounds, and the mean sojourn time are also given. Finally, some numerical examples to verify the conclusions are presented.