Fluid Analysis of Queueing in Two-Stage Random Environments
Fluid Analysis of Queueing in Two-Stage Random Environments
复制标题
两阶段随机环境中排队的流体分析
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
M. Tribastone
中科院分区：
文献类型：
--
作者：
G. Casale;M. Tribastone
大量随机环境导致马尔可夫过程，其中平均环境（AVG）和近完全分解（DEC）近似遭受不可接受的大误差。这对于排队网络来说尤其成问题，因为状态空间爆炸阻碍了数值方法的应用。本文介绍了一种新的基于流体的混合算法，用于随机环境下的排队模型。这里首先介绍的是随机环境的两个阶段。混合通过迭代评估每个阶段的瞬态分析子问题来估计模型的平衡。每个子问题都是通过一个非常小的常微分方程组来解决的，这使得该方法可扩展且易于实现。混合所支持的随机环境要么是独立于状态的（如具有故障和修复的模型），要么是依赖于状态的（如马尔可夫调制队列，其中服务阶段仅在繁忙期间更改）。与AVG和DEC近似的比较结果证明，混合解决了现有方法在随机环境中评估队列的局限性。
A large number of random environments leads to Markov processes where average-environment (AVG) and near-complete-decomposability (DEC) approximations suffer unacceptably large errors. This is problematic for queueing networks in particular, where state-space explosion hinders the application of numerical methods. In this paper we introduce blending, a novel fluid-based approximation for queueing models in random environments. The technique is here first introduced for random environments with two stages. Blending estimates the equilibrium of the model by iteratively evaluating transient-analysis sub problems for each of the two stages. Each sub problem is solved by means of a very small system of ordinary differential equations, making the approach scalable and simple to implement. Random environments supported by blending are either state-independent, as for models with breakdown and repair, or state-dependent, such as for Markov-modulated queues where the service phase changes only during busy periods. Comparative results with AVG and DEC approximations prove that blending tackles the limitations of existing methods for evaluating queues in random environments.