论文标题

受控高速公路基于线性编程的疏散模型

Linear programming based evacuation models for a controlled freeway

论文作者

He, Shengxue

论文摘要

提出了线性编程(LP)模型,以提高紧急撤离期间受控高速公路的性能。基于合理的假设,关键因素之间的主要关系在此模型中没有下属因素的不确定影响。解决了与最佳高速公路控制有关在紧急撤离期间有关的三个重要问题。如何通过对目标函数系数的敏感性分析来分析如何正确实现在紧急撤离期间分配给某些坡道的一些预定优先级。通过使用对相应约束的右侧(RHS)的灵敏度分析,还可以解决高速公路主线的时变吞吐能和坡道的存储能力。我们关注的最后一个关键问题是如何通过应用强大的优化来应对原油的不确定需求。本文提出的方法可以帮助疏散经理实现协调的坡道计量,并在紧急撤离期间进行了一些预定的优先事项。通过分析时间变化的主线容量的影响获得的结果为疏散经理提供了利用主线某些细分市场的额外容量来缓冲流量,以减少与上游坡道相关的拥塞。为了降低由于不确定情况下确定性控制方法的可能性而导致的风险,我们采用了可调节的强大对应方法(AARC)方法来处理不确定的动态需求,仅限于多面体集合。初步数值实验表明,AARC方法与基于采样的随机方法相比,为我们提供了有希望的解决方案。

A linear programming (LP) model is proposed to improve the performance of a controlled freeway during an emergency evacuation. Based on reasonable assumptions, the main relationships among key factors are kept without the uncertain impact of subordinate factors in this model. Three vital issues related to optimal freeway control during an emergency evacuation are addressed. How to properly realize some predetermined priorities assigned to some on-ramps during an emergency evacuation is analyzed through sensitivity analysis of objective function coefficients. The time-varying throughput capacity of freeway mainline and the storage capacities of on-ramps are also addressed by using sensitivity analysis of the right-hand side (RHS) of corresponding constraints. The last key issue we focused on is how to deal with the uncertain demand in a crude form by applying robust optimization. The methodology presented in this paper can help evacuation managers realize a coordinated ramp metering with predetermined priorities put on some on-ramps during an emergency evacuation. The result obtained by analyzing the impact of time-varying mainline capacity provides the evacuation manager a chance of using the extra capacity in some segments of mainline to buffer the traffic so as to reduce the congestion related to upstream on-ramps. To reduce the risk due to the possible infeasibility of deterministic control approaches in an uncertain situation, we apply an affinely adjustable robust counterpart (AARC) approach to deal with uncertain dynamic demands restricted to polyhedral sets. The preliminary numerical experiments show that the AARC approach provides us with a promising solution comparing to the sampling based stochastic approach.

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