带单重工作休假和休假中断的M/G/1排队系统

M/G/1 Queue with Single Working Vacation and Vacation Interruption

研究单重工作休假和休假中断的M/G/1排队系统,得到了其嵌入Markov链的转移概率矩阵,采用M/G/1型结构矩阵解析法,得到离去时刻稳态队长的母函数的解析表达式.采用经典随机分解方法,给出了队长的条件随机分解结构、条件等待时间的随机分解结果、稳态等待时间的LST变换及稳态下平均等待时间等性能指标.给出数值例子,并讨论了系统参数对几个主要性能指标的影响,从而验证了理论分析的合理性和有效性.

An M/G/1 queue system with a single working vacation and working interruption was studied. An M/G/1-type transition probability matrix of the embedded Markov chain was obtained. And using the M/G/1-type matrix analysis method, the PGF of the stationary queue length for the customers at departure epochs was derived. By the classic stochastic decomposition solution, the stochastic decomposition resuits of the stationary queue length and the conditional waiting time were presented. And some performance measures of the system such as the LST of the stationary waiting time and the expected waiting time were also obtained. Numerical examples were presented to show the influence of the system parametes on several main performance characteristics, and the rationality and the effectiveness of the theoretical analysis were proved.