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Extends the simplet transportation network model proposed in Nait-Sidi-Moh et al. (2002). We are interested in a public transportation system composed of several lines and several connection stops. The performance analysis and the evaluation of the travelling times at the connection stops are the main objectives of this study. Then to reach these goals we use a subclass of Petri nets to model our transportation network. By taking into account the network working, some structural conflicts appear in the graphical model. Then we solve them by determining routing equations. We represent our model by a non-stationary linear ( max, plus) system in the (max, plus) algebra. The resolution of this state model enables us to evaluate the system performances. Finally a numerical example is presented to illustrate the proposed model.