中英文对照论文-2005美赛B题The Booth Tolls for Thee_收费站模型
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After presenting this basic model, a more general, macroscopic framework for analyzing toll plaza design is introduced. In analyzing “total cost” and allowing bottlenecking, this model is more complete than the first, and it is able to make recommendations for booth number based on data obtained from the first model. This computation melds the macro- and micro- levels, a strategy that is helpful in looking at toll booth sitnt of the Problem / 问题重述
In fact, the models mostly agree that given L lanes, a number of booths around B = ⌊1.65L + 0.9⌋, where ⌊x⌋ is the greatest integer less than x, will minimize the total human cost associated with the plaza.
The Booth Tolls for Thee
Adam Chandler Matthew Mian Pradeep Baliga 翻译: 周吕文0
COMAP Mathematical Contest in Modeling February 7, 2005 Duke University
0本文的注解和排版由周吕文 (zhou.lv.wen@) 完成, 并仅限本人课程使用. 发现翻译错误或改进方案请发邮件告知.
在给出这样一个基本模型后, 本文介绍了一个用来分析 收费站广场设计的更通用的宏观模型. 在 “总成本” 的分析 和瓶颈的考虑方面, 这个模型较第一个模型更为完善, 并且该 模型能够基于第一个模型的数据给出建议的收费亭数量. 这 个计算融合了宏观和微观, 是一个有助于寻找收费亭的最优 数量的方法.
最终, 车流经过收费站广场的过程被表述为一个 “元胞 自动机” 模型. 作为一个着眼于微观的有趣的想法, 元胞自动 机模型可以用来对本文其它模型的独立验证.
本文解决有关车辆在收费站广场排队, 阻塞和堵车时大 量积压的问题. 我们考虑了多种模型来最小化 “系统成本”, “系统成本” 包括司机浪费的时间价值和收费站每天的运营 成本.
第一个模型给出了一个微观模拟, 该模拟能够描述当服 务率不能满足需求时, 收费站广场前将形成队列. 应用新泽 西州某个主干道每小时的需求数据, 这个模拟的缺限在于没 有考虑瓶颈效应. 然而, 通过阈值分析表明这个模型的结果 可以作为收费亭需求数量的上界, 并有可能为其它模型提供 参考.
Finally, a model for traffic flow through a plaza is formulated in the world of “cellular automata”. An interesting take on microscopic ideas, the cellular automata model can serve as an independent validation of our other models.
事实上, 三个模型几乎都给出同样的结论: 对于 L 条车 道, 收费亭的数量为 B = ⌊1.65L + 0.9⌋ 时, 与收费站广场相 关的人力总成本将达到最小, 其中 ⌊x⌋ 返回的是大于 x 的最 小整数.
Team number 770
翻译:周吕文
Page 1 of 60
Contents
1 Introduction / 引言
Abstract
In this paper, we address the problems associated with heavy demands on toll plazas such as lines, backups, and traffic jams. We consider several models in hopes of minimizing the “cost to the system”, which includes the time-value of time wasted by drivers as well as the cost of daily operations of the toll plaza.
One model yields a microscopic simulation of line formation in front of the toll booths when the service rate cannot match the demand. Using hourly demand data from a major New Jersey parkway, the simulation is limited in not taking bottlenecking effects into consideration. The results, however, when subjected to threshold analysis can serve to set upper bounds on the number of booths that could potentially be suggested by any other models.
In fact, the models mostly agree that given L lanes, a number of booths around B = ⌊1.65L + 0.9⌋, where ⌊x⌋ is the greatest integer less than x, will minimize the total human cost associated with the plaza.
The Booth Tolls for Thee
Adam Chandler Matthew Mian Pradeep Baliga 翻译: 周吕文0
COMAP Mathematical Contest in Modeling February 7, 2005 Duke University
0本文的注解和排版由周吕文 (zhou.lv.wen@) 完成, 并仅限本人课程使用. 发现翻译错误或改进方案请发邮件告知.
在给出这样一个基本模型后, 本文介绍了一个用来分析 收费站广场设计的更通用的宏观模型. 在 “总成本” 的分析 和瓶颈的考虑方面, 这个模型较第一个模型更为完善, 并且该 模型能够基于第一个模型的数据给出建议的收费亭数量. 这 个计算融合了宏观和微观, 是一个有助于寻找收费亭的最优 数量的方法.
最终, 车流经过收费站广场的过程被表述为一个 “元胞 自动机” 模型. 作为一个着眼于微观的有趣的想法, 元胞自动 机模型可以用来对本文其它模型的独立验证.
本文解决有关车辆在收费站广场排队, 阻塞和堵车时大 量积压的问题. 我们考虑了多种模型来最小化 “系统成本”, “系统成本” 包括司机浪费的时间价值和收费站每天的运营 成本.
第一个模型给出了一个微观模拟, 该模拟能够描述当服 务率不能满足需求时, 收费站广场前将形成队列. 应用新泽 西州某个主干道每小时的需求数据, 这个模拟的缺限在于没 有考虑瓶颈效应. 然而, 通过阈值分析表明这个模型的结果 可以作为收费亭需求数量的上界, 并有可能为其它模型提供 参考.
Finally, a model for traffic flow through a plaza is formulated in the world of “cellular automata”. An interesting take on microscopic ideas, the cellular automata model can serve as an independent validation of our other models.
事实上, 三个模型几乎都给出同样的结论: 对于 L 条车 道, 收费亭的数量为 B = ⌊1.65L + 0.9⌋ 时, 与收费站广场相 关的人力总成本将达到最小, 其中 ⌊x⌋ 返回的是大于 x 的最 小整数.
Team number 770
翻译:周吕文
Page 1 of 60
Contents
1 Introduction / 引言
Abstract
In this paper, we address the problems associated with heavy demands on toll plazas such as lines, backups, and traffic jams. We consider several models in hopes of minimizing the “cost to the system”, which includes the time-value of time wasted by drivers as well as the cost of daily operations of the toll plaza.
One model yields a microscopic simulation of line formation in front of the toll booths when the service rate cannot match the demand. Using hourly demand data from a major New Jersey parkway, the simulation is limited in not taking bottlenecking effects into consideration. The results, however, when subjected to threshold analysis can serve to set upper bounds on the number of booths that could potentially be suggested by any other models.