A connected environment offers an effective solution to smart cities' current concerns. The performance of existing traffic signals and speed advisory technology can be improved by cooperation between traffic signal and speed system advisory in a connected environment. This research proposes a connected intersection where the traffic light and individual vehicles' speed can be optimized simultaneously. Traffic signal timing and arrival time of the vehicles at the beginning of each cycle can be calculated to find the optimum speed, brake force, and vehicle engine power each second. The main contribution of this thesis is to consider the optimization of the traffic signal and vehicles' velocity together at the same time at different penetration rates and demand levels to optimize total travel time, stop time, delay, and fuel consumption. Few research studies have considered these simultaneously. An analysis is conducted to compare the result of this thesis with actuated and fixed-time traffic signals. The results show improvement in fuel consumption and mobility, specifically at the lower demand levels.