The speed gradient (SG) model was extended to a mixture of different types of vehicles. The extended SG model was used to study the steady state of the mixed traffic flow system, the formation of traffic jams at a traffic light switching from green to red, the dissolution of jams at a traffic light switching from red to green, and the local cluster effect of the mixed traffic system. The simulation results are qualitatively consistent with everyday experience. DE: Cluster-analysis; Signalized-intersections; Speed-gradient-model; Steady-state; Traffic-congestion; Traffic-flow; Vehicle-mix