## 3 Methodology  
The review of contemporary works on the forecasting of crowds and traffic illustrates that especially recurrent neural networks are equipped to forecast crowd movements. Yet, up to this moment a RNN has never been applied for this purpose. Considering the work on traffic forecasting methods, the work of [15] is most in line with the objective of this study, namely the method forecasts a sequence of locations visited by a vehicle in a large street network. A great benefit of the approach presented by [15] is the very limited computational effort involved in data filtering and training. The use of smartly chosen cells instead of a directed graph consisting of nodes and links diminishes the computational effort greatly, as map-matching of GPS traces to the network is circumvented. Moreover, the use of a small number of cells that automatically adopt the structure of the transportation network, allows for a reasonably valid and logical discretization of the network. Yet, the approach cannot be adopted without changes as the movement patterns of visitors at event terrains differ in three ways from vehicular traffic during morning rush hour. Firstly, the temporal dimension of the movement pattern differs. That is, movement patterns at events are dependent on the stage programming which changes quickly throughout the entire day. Specifically at the beginning and end of programmed shows high flows arise that develop quickly and disappear just as fast. In order to catch these sudden increases and decreases of flow rates predictions at 5 min intervals instead of hours are needed from opening till closing time. Secondly, activities do not only occur at the nodes of a network, but also on the links in between. As a result, in contrast to the original approach, the crowd movement forecasting approach should be capable to predict stay-in-place traffic as well as traffic that moves through the corridors of the network. Thirdly, pedestrians at events do not disappear from the traffic network when they reach their location. Consequently, no identification of the end of a cell sequence is necessary. As a result of the differences in the traffic and crowd movement patterns, adaptations to the original approach presented by [15] are needed. The following section will detail the adapted forecasting approach. In essence, the approach consists of three steps, being: (1) the segmentation of space, (2) the identification of cell sequences and (3) the training of the RNN-GRU. As in this research the forecasting results of the RNN-GRU will be compared using six comparison models, namely three shallow neural networks and three Markov chain model that incorporate varying degrees of memory. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Memory Regarding Average Reaction** & **Memory Regarding Average** & **Memory Regarding the Dynamic State Transitions of the System** \\ \hline Linear & Kalman Filter (KF) & & ARIMA \\ \hline \multirow{4}{*}{Non-linearity} & Extended Kalman filter (EKF) & Hidden Markov Model (HMM) & Recurrent neural network with \\  & Particle Filter (PF) & Neural Network (NN) & gated recurrent unit (RNN-GRU) \\ \cline{1-1}  & Gaussian Maximum Likelihood (GML) & Support Vector Machine (SVM) & Recurrent neural network with long \\ \cline{1-1}  & & & short term memory (RNN LSTM) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Categorization of mathematical techniques for traffic forecasting. Furthermore, this research wants to test how valid the predictions by all seven models are, and whether the best forecasting model is capable of performing real-time predictions while an event is ongoing. Therefore, the research methodology also includes a cross- validation step and a test in which several additional data division methods and sequencing strategies are tested. The complete research methodology is visualized in Figure 1. The following paragraphs will elaborate on the steps of the research methodology.