Research Initiation: Perturbation Analysis of Networks withDynamic Routing Strategies

一段时间以来，排队论和仿真一直是研究离散事件动态系统(DEDS)的主要分析工具。这样的系统根据不同事件的发生而演变，这些事件以未知的、不规则的间隔发生，并且与过程状态的变化相关联。扰动分析显示了克服与经典排队理论和模拟技术相关的一些限制的前景。该方法采用排队网络的动态系统观点，本质上将状态方程线性化，利用离散事件驱动的性质来表征状态方程。这项研究的目的是研究更广泛的排队网络，在这些网络中，无穷小的参数扰动实际上会产生有限的排队长度扰动。在使用状态相关路由策略以提供灵活性和增强可靠性的网络中就是这种情况。对于这种动态路由策略的一类参数化类，将使用扰动分析来优化策略。结果的验证将通过使用适当的模拟模型来完成。对于具有封闭形式结果的简单排队系统，将开展对扰动解析性能梯度估计的统计性质的分析评估。

Queueing theory and simulation have for some time provided the main analytical tools in the study of discrete-event-dynamic systems (DEDS). Such systems evolve in accordance with the occurrence of distinct events which occur at unknown, irregular intervals and which are associated with a change in the state of the process. Perturbation analysis has shown promise for overcoming some of the limitations associated with both classical queueing theory and simulation techniques. This approach adopts a dynamic system viewpoint of queueing networks and essentially linearizes the state equations, characterizing them by exploiting their discrete-event-driven nature. The aim of this research is to investigate wider classes of queueing networks, where infinitesimal parametric perturbations actually create finite queue length perturbations. This is the case in networks with state dependent routing strategies used to provide flexibility and enhance reliability. For a parametrized class of such dynamic routing strategies, perturbation analysis will be used to optimize the strategy. Validation of the results will be accomplished through the use of appropriate simulation models. For simple queueing systems where closed-form results are available, work will be done to develop analytical evaluation of the statistical properties of perturbation analytic performance gradient estimates.