带休假延迟和启动时间的M/M/1多重休假排队系统分析

Analysis of multiple vacation M/M/1 queue with delayed vacation and setup time

考虑了带休假延迟和启动时间的M/M/1多重休假排队系统,运用QBD过程和矩阵几何解等工具,给出过程稳态队长的具体形式,在此基础上,推导出稳态条件下队长和平稳等待时间的随机分解结构以及系统的附加队长分布和附加延迟LST的具体形式.并进一步得到系统处在各种状态的概率和稳态指标的均值。

This paper considers an M/M/1 queue system with multiple vacation,delayed vacation and setup time. By apply- ing quasi-birth-death （QBD） process and matrix-geometric solution method, the analytic expression of the stationary queue length and stochastic decomposition structures of the stationary queue length and waiting time are given. Meanwhile, it is demonstrated that the additional queue length and the expression of the laplace-stieltjes transformation of additional delay. Moreover, expectation of stationary indices, the steady state probabilities that the system in vacation delay, vacation period, setup time and busy period are calculated respectively.