Presentation of regression analysis, GP and GMDH models to predict the pedestrian density in various urban facilities

In this study, the relationship between space mean speed (SMS), flow rate and density of pedestrians was investigated in different pedestrian facilities, including 1 walkway, 2 sidewalks, 2 signalized crosswalks and 2 mid-block crosswalks. First, statistical analysis was performed to investigate the normality of data and correlation of variables. Regression analysis was then applied to determine the relationship between SMS, flow rate, and density of pedestrians. Finally, two prediction models of density were obtained using genetic programming (GP) and group method of data handling (GMDH) models, and k-fold and holdout cross-validation methods were used to evaluate the models. By the use of regression analysis, the mathematical relationships between variables in all facilities were calculated and plotted, and the best relationships were observed in flow rate-density diagrams. Results also indicated that GP had a higher R-2 than GMDH in the prediction of pedestrian density in terms of flow rate and SMS, suggesting that GP was better able to model SMS and pedestrian density. Moreover, the application of k-fold cross-validation method in the models led to better performances compared to the holdout cross-validation method, which shows that the prediction models using k-fold were more reliable. Finally, density relationships in all facilities were obtained in terms of SMS and flow rate.