具有相型服务分布的排队系统的性能灵敏度分析

具有非线数服务分布的排队网络已被广泛应用于许多领域，如通讯网络和管理系统。本文借助于无穷小说矩阵摄动方法，研究了M/PH/1排队系统的稳态性能灵敏度分析问题，给出了性能灵敏度公式，并表明了稳态性能灵敏度很容易通过系统势能进行计算。同时，给出一种计算势能及性能导数的算法。这个算法可直接用于系统的控制与优化，因为它基于分析系统的一条单一样本轨道。最后提供一个数值例子来表明这个算法的应用。

Sensitivity Analysis of Performance in Queueing Systems with Phase-Type Service Distributions

The queueing networks with nonexponential service distributions have been widely applied in many areas, such as communication networks and management systems. In this paper, by using the approach of infinitesimal generator perturbation, we study the problems of sensitivity analysis of the steady-state performance for M/PH/1 queueing systems. Sensitivity formulas of performance are given. It is shown that sensitivity of the steady-state performance can be easily calculated by using the potentials of systems.An algorithm to compute potentials and performance derivatives is proposed. This algorithm can be directly used in controlling and optimization problems, because it bases on analyzing a single sample path of a queueing system. A numerical example is provided to illustrate the application of the algorithm.