Intelligent transportation system (ITS) uses electronic technologies such as information and communication technologies to improve the efficiency of transportation management. In the theoretical framework of gas-kinetic traffic flow model, the probability of capable passing is essential for ITS. The probability of capable passing is assumed be a linear function of the traffic concentration, indicating that the probability of capable passing decreases proportionally with an increasing concentration. This work improves the model by introducing the speed desired by the driver into the original two-lane cellular automata (CA) model. This study also examines the accuracy of the linearity assumption. A capable passing principle is established to simulate the capable passing probability for different concentrations and can be embedded in a system on chip of ITS.