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Macroscopic arterial traffic flow modeling is crucial for signal control because most of signal control systems are relying on macroscopic models to quickly generate performance to evaluate control strategies. However, because of the randomness of vehicle speed, most of the macroscopic models are lack of capability to adequately reproduce the stochastic nature of traffic dynamics, especially for arterials with actuated signal control. To solve this problem, this research proposed a new model that incorporates a simplified shockwave model with traffic diffusion theory, which is able to reproduce the stochastic nature of traffic dynamics. The simulation results and comparison with field observed data verify that the proposed model is not only to model the traffic dynamics on arterials, but it is also able to derive signal timings of actuated intersections. Such results are encouraging since this model can be applied to a variety …