Iterative analysis of networks of queues
Iterative analysis of networks of queues
复制标题
队列网络的迭代分析
DOI：
--
复制
发表时间：
1984
期刊：
影响因子：
--
通讯作者：
R. Walstra
中科院分区：
文献类型：
--
作者：
R. Walstra
队列网络研究的主要推动力是这种网络与计算机系统性能研究的相关性。随着排队网络理论的发展，从建模研究中产生的网络往往越来越复杂。其结果是，队列网络的精确解可能变得过于昂贵。因此，排队网络的近似分析方法已成为人们主要感兴趣的研究领域。
在本文中，我们将提出一个基于网络分解的排队网络近似分析框架。在分解分析中，排队网络的性能指标是从一个联立的非线性方程组的解得到的。通常，此解是通过不动点迭代获得的。特别地，我们将关注具有非指数服务时间分布的闭合排队网络的迭代分析和FCFS调度，并利用最大熵原理，提出了一种新的迭代分析方法。
我们将证明我们的熵最大化方法，第一，给出了可分排队网络的精确结果，第二，给出了满足基本工作速率定理的近似结果，第三，给出了用指数级方法来表示非指数服务时间分布的全局平衡方程组所获得的可能的性能范围的界。考虑到执行时间的要求，我们的方法提供了一种可行的替代齐次近似方法，在齐次近似方法中，非指数服务时间分布是用带有条件平均值的指数分布来估计的。
The major impetus for the study of networks of queues is the relevance of such networks to performance studies of computer systems. As the theory of networks of queues evolves, networks which arise from modeling studies tend to be of increasing complexity. As a consequence, exact solutions of networks of queues can become excessively expensive. Methods for the approximate analysis of networks of queues have therefore become a research area of major interest.
In this thesis we will propose a framework for the approximate analysis of networks of queues based on network decomposition. In the analysis by decomposition, performances measures of a network of queues are obtained from the solution of a system of simultaneous nonlinear equations. Typically, this solution is obtained by fixed point iteration. In particular, we will be concerned with the iterative analysis of closed networks of queues with nonexponential service time distributions and FCFS scheduling, and, using the Principle of Maximum Entropy, we will propose a new technique for the iterative analysis of such networks of queues.
We will show that our method of entropy maximization, first, produces exact results for separable networks of queues, second, yields approximate results which satisfy the fundamental work rate theorem, and, third, gives rise to bounds on the range of possible performance obtained by solving a system of global balance equations using the method of exponential stages to represent nonexponential service time distributions. Considering execution time requirements, our method offers a viable alternative to the homogeneous approximation method in which nonexponential service time distributions are estimated by exponential distributions with conditional mean values.