带启动时间和休假延迟的Geom/Geom/1排队模型

The Geom/Geom/1 Queue Model with Setup Time and Delayed Vacation

由于在计算机网络、通讯系统、生产交通领域建模的广泛应用,离散时间休假排队成为近年来应用概率的一个研究热点。考虑带休假延迟和启动时间的Geom/Geom/1多重休假排队系统,运用QBD链和矩阵几何解等工具,给出过程稳态队长分布的具体形式,在此基础上,推导出平稳状态下队长与逗留时间的随机分解结构,并进一步得到系统在相应状态下的概率和稳态指标的均值。

This paper considers a Geom/Geom/1 queueing system with multiple vacation, delayed vacation and setup time. By applying quasi -birth -death chain and matrix -geometric solution method, the analytic expres- sion of the stationary queue length is given. Meanwhile, it has demonstrated the stochastic decomposition struc- tures of the stationary queue length and sojourn time. 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.