离散时间有限缓冲空间GI/Geom/1/N工作休假排队系统稳态概率算法及性能分析

Steady-state probability algorithm and performance analysis of the finite buffer discrete-time GI/Geom/1/N queueing system with working vacations

综合使用离散补充变量方法和嵌入Markov链技术研究了离散时间有限缓冲空间工作休假GI/Geom/1/N排队系统.首先运用离散补充变量方法给出一个重要等式,从而获得系统在稳态情形下任意时刻队长分布和顾客到达前夕队长分布的迭代关系.然后,再利用嵌入Markov链技术通过求解不变概率测度方程获得顾客到达前夕队长分布的数值解.而后将顾客到达前夕队长分布代入迭代公式求得稳态情形下任意时刻的队长分布.最后给出几个特殊情形下的数值计算实例,并讨论了系统参数对几个主要性能指标的影响.

Applying the method for discrete supplementary variable and embedded Markov chain technique, we investigate a finite buffer discrete-time GI/Geom/1/N qneueing system with working vacations. First, by employing the discrete supplementary variable technique, we give an important equation, and then we obtain the iterative relationship between the steady-state queue length distribution at prearrival and arbitrary epochs. Second, using the embedded Markov chain technique and solving the invariant probability measure equation, we get the numerical solutions for queue length distribution at prearrival. Furthermore, using the queue length distribution at prearrival and iterative formula, the steady-state queue length distribution at arbitrary epochs are obtained. At last, we present a numerical example under a special case and study the influence of the system parameters on several performance characteristics.