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Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results
Transportation Research Part C: Emerging Technologies ( IF 8.3 ) Pub Date : 2023-01-31 , DOI: 10.1016/j.trc.2023.104036
Jorge A. Laval

This paper presents additional results of the generalized bathtub model for urban networks, including a simpler derivation and exact solutions for uniformly distributed trip lengths. It is shown that in steady state this trip-based model is equivalent to the more parsimonious accumulation-based model, and that the trip-length distribution has merely a transient effect on traffic dynamics, which converge to the same point in the macroscopic fundamental diagram (MFD). To understand the statistical properties of the system, a queueing approximation method is proposed to compute the network accumulation variance. It is found that (i) the accumulation variance is much larger than predicted by traditional queueing models, due to the nonlinear dynamics imposed by the MFD, (ii) the trip-length distribution has no effect on the accumulation variance, indicating that a proposed formula for the variance might be universal, and (iii) the system exhibits critical behavior near the capacity state where the accumulation variance diverges. This indicates that the tools from critical phenomena and phase transitions might be useful to understand congestion in cities.



中文翻译:

行程长度分布对网络级交通动态的影响:精确和统计结果

本文介绍了城市网络广义浴缸模型的其他结果,包括更简单的推导和均匀分布行程长度的精确解。结果表明,在稳态下,这种基于行程的模型等效于更简约的基于累积的模型,并且行程长度分布对交通动态仅具有瞬态影响,在宏观基本图中收敛到同一点(制造商)。为了理解系统的统计特性,提出了一种排队近似方法来计算网络累积方差。发现 (i) 由于 MFD 施加的非线性动力学,累积方差比传统排队模型预测的大得多,(ii) 行程长度分布对累积方差没有影响,表明建议的方差公式可能是通用的,并且(iii)系统在累积方差发散的容量状态附近表现出临界行为。这表明来自临界现象和相变的工具可能有助于了解城市拥堵。

更新日期:2023-02-01
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