Prediction of accurate travel time plays an important role in dynamic route guidance on urban networks. The dynamic traffic flows entering the network affect the behavior of the system and the free flow movement of vehicles. To study the complex system dynamics of an urban network under varying input flows, we begin with the basic unit of the network called a lane. The analysis of the behavior of a single lane is done to derive the travel time from the characteristics of the lane, the input flow and the constraints on the output flow. The system analysis of the single lane is then applied to the whole network for studying the transfer of flows inside the network. A dynamic network model has been proposed for the network analysis. A simulation software has been developed using the dynamic network model which generates travel times on the network using the input data as the flows coming at the entrances of the system, the initial system states of the lanes and the characteristics of the network.