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Time dependent queuing models of the national airspace system .

机译:国家空域系统的时间依赖排队模型。

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摘要

Air transportation in the US system has dramatically changed in the past few decades. The National Airspace System (NAS) has increasingly become congested. A high volume of air traffic demand is one of the major challenges of the NAS. However, air traffic is very difficult to study due to many uncertainties involved. It is important that we be able to understand the relationship under uncertainties due to aviation operations, precision of navigation and control, and traffic flow efficiency. Many queuing models have been studied to better understand and quantify these relationships. In the past decade, most queuing network models assume that inter-arrival times and service times are exponentially distributed and stationary, which may not be suitable for all scenarios. These queuing models are time invariant and have several drawbacks. In particular, they do not account for increases and decreases in demand that are commonly observed in the NAS throughout a day. Previously, the NAS has been studied and analyzed by using traditional Makovian queues. However, observations from simulations of real traffic data reveal that the inter-arrival time and service time probability distributions cannot be represented by exponential probability density functions. The Coxian distribution is a phase-type distribution that has gained special importance in the research on queuing networks. In this study, several methods of fitting Coxian distribution to data together with different time dependent queuing models of the NAS are developed and discussed.;In the past few decades, Coxian distributions have become increasingly more popular. The probability distribution functions for inter-arrival times/service times of airspace systems cannot be represented by traditional probability distribution functions. In the first part of this dissertation, we describe different algorithms to fit Coxian distributions to the service times of major Air Traffic Centers. Several fitting methods are developed and discussed. Finally, we compare and evaluate those methods by using the mean square error (MSE) and the number of phases in the distribution.;In the second part of this dissertation, we discuss a practical approach for modeling the NAS with time-dependent Coxian queues. Time-dependent Cm(t)(t)/Ck/s queuing models of the National Airspace are developed in which the inter-arrival distribution is a time-dependent piece-wise constant Coxian random variable, and the service time distribution is a Coxian random variable. We describe an algorithm for calibrating a Cm(t)(t)/Ck/s queuing model from simulated data of an Air Route Traffic Control Center and an algorithmic approach to determine average measures of the queues. Finally, we give future directions for studying such queuing models.
机译:在过去的几十年中,美国系统中的航空运输发生了巨大变化。国家空域系统(NAS)越来越拥挤。大量的空中交通需求是NAS的主要挑战之一。但是,由于涉及许多不确定因素,空中交通很难研究。重要的是,我们必须了解由于航空运营,导航和控制的精度以及交通流效率而导致的不确定性之间的关系。已经研究了许多排队模型以更好地理解和量化这些关系。在过去的十年中,大多数排队网络模型都假设到达间隔时间和服务时间呈指数分布且固定不变,这可能并不适合所有情况。这些排队模型是时不变的,并且具有几个缺点。特别是,它们无法解决一天中通常在NAS中观察到的需求的增加和减少。以前,已经使用传统的马氏队列对NAS进行了研究和分析。然而,从真实交通数据的模拟观察中发现,到达时间和服务时间的概率分布不能用指数概率密度函数表示。考克斯分布是一种相型分布,在排队网络的研究中已变得尤为重要。在这项研究中,开发并讨论了几种将Coxian分布拟合到数据以及NAS的不同时间依赖排队模型的方法。在过去的几十年中,Coxian分布变得越来越流行。空域系统到达时间/服务时间的概率分布函数不能用传统的概率分布函数表示。在本文的第一部分中,我们描述了不同的算法,以将Coxian分布拟合到主要空中交通中心的服务时间。开发并讨论了几种拟合方法。最后,我们利用均方误差(MSE)和分布中的相数来比较和评估这些方法。在本论文的第二部分中,我们讨论了一种使用时变Coxian队列对NAS进行建模的实用方法。 。建立了国家空域的时间相关Cm(t)(t)/ Ck / s排队模型,其中到达间隔分布是时间相关的分段常数Coxian随机变量,服务时间分布是Coxian随机变量。我们描述了一种从空中交通管制中心的模拟数据中校准Cm(t)(t)/ Ck / s排队模型的算法,以及一种确定队列平均度量的算法方法。最后,我们给出了研究这种排队模型的未来方向。

著录项

  • 作者

    Roongrat, Chatabush.;

  • 作者单位

    The University of Texas at Arlington.;

  • 授予单位 The University of Texas at Arlington.;
  • 学科 Statistics.;Operations Research.;Transportation.
  • 学位 Ph.D.
  • 年度 2011
  • 页码 90 p.
  • 总页数 90
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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