Connected vehicles enabled by communication technologies have the potential to improve traffic mobility and enhance roadway safety such that traffic information can be shared among vehicles and infrastructure. Fruitful speed advisory strategies have been proposed to smooth connected vehicle trajectories for better system performance with the help of different car-following models. Yet, there has been no such comparison about the impacts of various car-following models on the advisory strategies. Further, most of the existing studies consider a deterministic vehicle arriving pattern. The resulting model is easy to approach yet not realistic in representing realistic traffic patterns. This study proposes an Individual Variable Speed Limit (IVSL) trajectory planning problem at a signalized intersection and investigates the impacts of three popular car-following models on the IVSL. Both deterministic and stochastic IVSL models are formulated, and their performance is tested with numerical experiments. The results show that, compared to the benchmark (i.e., without speed control), the proposed IVSL strategy with a deterministic arriving pattern achieves significant improvements in both mobility and fuel efficiency across different traffic levels with all three car-following models. The improvement of the IVSL with the Gipps’ model is the most remarkable. When the vehicle arriving patterns are stochastic, the IVSL improves travel time, fuel consumption, and system cost by 8.95%, 19.11%, and 11.37%, respectively, compared to the benchmark without speed control.