GI/G/1系统等待时间分布的数值近似法

Numerical approximation of waiting time distribution in a GI/G/1 system

求解排队系统的等待时间分布对于系统规划及性能分析具有重要意义 ,在排队系统 (GI/G/1)中这一问题通常难以得到显式的理论解。从该问题的 Wiener- Hopf积分方程出发 ,利用排队系统的固有特征将问题转化为一个线性方程组 ,并讨论了使用迭代法求解该方程组的收敛性和复杂度。文中给出了几种系统模型下的数值实验数据 ,并与已有方法进行了比较 ,结果表明 :该方法在不同模型、不同负载下均能给出精确的计算结果 ,实验中通过合理选择计算参数可将误差控制在 0 .0 5 %以内。该方法易于实现、计算效率高 ,具有较好的实用性。

Waiting time distribution is of great importance in the analysis of queueing systems. However, a closed form solution is not easily obtained for a GI/G/1 system. A proposed numerical approximation method for calculating the distribution density is characterized by approximating the Wiener Hopf equation with a system of linear equations that are solved iteratively. The convergence and the complexity of the algorithm are analyzed in the paper. Numerical experiments with several queueing models show that the method yields accurate results for various loads and system parameters, with the approximating error less than 0.05% with optimized calculational parameters. Compared to previous methods in the literature, this algorithm provides better accuracy, efficiency and ease of implementation.