论文标题
基于分散指标的强大排队网络分析仪
A Robust Queueing Network Analyzer Based on Indices of Dispersion
论文作者
论文摘要
我们开发了一种强大的排队网络分析仪算法，以近似具有马尔可夫路由的单人队列单级排队网络的稳态性能。该算法允许非更新外部到达流程，一般服务时间分布和客户反馈。我们专注于客户流量，定义为计算客户流入或流出网络或从一个队列流向另一个队列的连续时间流程。每个流的部分都以其速率和连续函数来衡量随时间的随机变异性。此函数是方差时间曲线的缩放版本，称为计数（IDC）的分散索引。可以从模型基底物计算出所需的IDC函数，该功能可以根据数据估算或通过求解一组线性方程来估算。强大的排队技术用于从总到达流的IDC和该队列的服务规范中生成平均稳态性能的近似值。广泛的模拟研究和繁重的限制支持算法效率。
We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival processes, general service-time distributions and customer feedback. We focus on the customer flows, defined as the continuous-time processes counting customers flowing into or out of the network, or flowing from one queue to another. Each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance-time curve, called the index of dispersion for counts (IDC). The required IDC functions for the flows can be calculated from the model primitives, estimated from data or approximated by solving a set of linear equations. A robust queueing technique is used to generate approximations of the mean steady-state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm effectiveness is supported by extensive simulation studies and heavy-traffic limits.
