Public transportation stands a very important role in the modern society. It solves many transportation problems, reduces the negative impacts of motor vehicles to the environment, and brings benefit and mobility to everyone. Public transportation models are used in urban area transit networks in order to predict the future impacts of the traffic policy and changes. Models in public transportation simulation are extensively studied in the literature, but very few have compared all the available models to a traffic data to find which model is the most accurate one in simulating a transit network. This study provides an overview of some of the available approaches in public transportation modeling, describes how they work by both theoretical review and examples. On the analysis, the modeling results from each model are compared with the Stockholm traffic data. The Stockholm traffic data of average weighted travel time, travel distance, in-vehicle travel distance and number of transfers are extracted from the RES05/06 survey data. The model which provides modeling outputs with least root mean square error compared to the survey data is found. This study could give an initial suggestion for the same type of transit modeling in choosing the appropriate model and finding the direction for calibrating the parameter settings through our proposed comparison measures.