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We study the LWR model and a conserved higher-order model on a road network.The Riemann problem at a junction for each model is discussed, which is crucial to construct numerical schemes.By using different numerical flux on roads and the exact Riemann solution at a junction, several first-order schemes are designed.Two numerical examples are given to show the schemes for the LWRmodel and a conserved higher-order model on a road network are feasible.