## 1 Introduction
When ramp metering was implemented, higher flows were observed for accumulation values after capacity, and without it, higher accumulation values were reached. The onset and offset of congestion can produce loops (even more than one), and rapid changes in demand affect the MFD. When the demand decreased sharply, lower flows were observed in the congestion recovery than during the congestion evolution (when accumulation was increasing). A bifurcation in the MFD (average network density vs. average network flow) was detected (considering weekdays) in [26]; in the MFD, a pattern in the morning peak and a different pattern in the evening peak could be distinguished. The identified cause of the bifurcation was that in the morning, drivers follow an efficient path (likely because they are going to work), and in the evening drivers take detours. In an arterial signalized intersection, a different capacity value was observed in the AM peak than in the PM peak [27]. The reasons for this were the ratio between green time and the traffic cycle time, signal coordination, and turning movements. Also, it was found that the scatter in the arterial fundamental diagram (AFD, represented as occupancy vs. flow) disappears if the Queue-Over-Detector (QOD, which is the phenomenon in which a vehicle is over the detector because the queue formed during the red time) is removed. In the absence of QOD, a stable AFD appears with three identifiable regimes: under-saturation, saturation, and over-saturation. The result of modifying the cycle length (or the offset) is that the MFD capacity changes [28]. The relation between accumulation and the trip completion rate was investigated in [29], an analytically derived Markov Chain framework was proposed to explain aggregate network dynamics, which was capable of accounting for uncertainties. The shape of an MFD (traffic density per unit of area vs. space mean speed over a time period) depends on the network' topologies, as was evidenced in [30] with 63 networks; the space mean speed was explained with the macroscopic Underwood model, which has as parameters the free-flow space mean speed and the optimal traffic density per unit of area. These are explained in turn with the average number of junctions per unit distance (which captures the stop-and-go frequency of the vehicles) and with the degree density normalized by the trafficable area (which captures the intensity of conflicts between vehicles), respectively. The relation between the MFD properties and the structure of the road network is described [31]. The effects of signal coordination on the MFD were investigated in [32], which stated that the impacts of the strategies were sensitive to the signal cycle length chosen (60 s, 90 s, 120 s), and a poor signal coordination reduces the network capacity and the free-flow speed. Other variables that affect the MFD include junction regulation [33], traffic signals [34; 35; 36], network spatial characteristics [37], buses [38], large-scale activities [39], autonomous vehicles [40; 41; 42; 43], turning traffic [44], rainfall [45], ride pooling [46], bicycle traffic [47], traffic incidents [48], the position of the loop detectors [49], and network heterogeneity [50]. As presented in the literature above, there are a lot of variables that can impact the MFD. However, a method to establish if a variable has impacts on the MFD is lacking. Moreover, it has yet to be determined which variables from a selected set affect the MFD. Thus, the aim of this work is to design a method to determine if a proposed variable modifies the MFD shape. A brief introduction of the method is as follows. For each variable selected, an experiment is conducted. During each experiment, a simulation is performed for each value (or configuration) the variable takes, and a MFD model is constructed with the aggregated data from each simulation. We compare the simulations by establishing a metric distance between density vs. speed patterns, between capacities, and between critical densities.