The Macroscopic Fundamental Diagram (MFD) describes the relation of average network flow, density and speed in urban networks. It can be estimated based on empirical or simulation data, or approximated analytically. Two main analytical approximation methods to derive the MFD for arterial roads and urban networks exist at the moment. These are the method of cuts (MoC) and related approaches, as well as the stochastic approximation (SA). This paper systematically evaluates these methods including their most recent advancements for the case of an urban arterial MFD. Both approaches are evaluated based on a traffic data set for a segment of an arterial in the city of Munich, Germany. This data set includes loop detector and signal data for a typical working day. It is found that the deterministic MoC finds a more accurate upper bound for the MFD for the studied case. The estimation error of the stochastic method is about three times higher than the one of the deterministic method. However, the SA outperforms the MoC in approximating the free-flow branch of the MFD. The analysis of the discrepancies between the empirical and the analytical MFDs includes an investigation of the measurement bias and an in-depth sensitivity study of signal control and public transport operation related input parameters. This study is conducted as a Monte-Carlo-Simulation based on a Latin Hypercube sampling. Interestingly, it is found that applying the MoC for a high number of feasible green-to-cycle ratios predicts the empirical MFD well. Overall, it is concluded that the availability of signal data can improve the analytical approximation of the MFD even for a highly inhomogeneous arterial.

宏观基本原理图（MFD）描述了城市网络中平均网络流量，密度和速度之间的关系。可以根据经验或模拟数据进行估算，也可以通过分析得出近似值。目前，存在两种主要的分析近似方法来推导主干道和城市网络的MFD。这些是削减方法（MoC）和相关方法，以及随机逼近（SA）。本文系统地评估了这些方法，包括针对城市动脉MFD的最新进展。两种方法均基于德国慕尼黑市某段动脉的交通数据集进行评估。该数据集包括典型工作日的环路检测器和信号数据。发现确定性MoC为研究案例找到了MFD的更准确的上限。随机方法的估计误差约为确定性方法之一的三倍。但是，SA在逼近MFD的自由流分支方面胜过MoC。对经验MFD与分析MFD之间差异的分析包括对测量偏差的调查以及对信号控制和公共交通运营相关输入参数的深入敏感性研究。这项研究是基于拉丁文Hypercube采样的蒙特卡罗模拟法进行的。有趣的是，发现将MoC用于大量可行的绿色循环比可以很好地预测经验MFD。总体，