Consecutive traffic signalized intersections can increase vehicle stops, producing vehicle accelerations on arterial roads and potentially increasing vehicle fuel consumption levels. Eco-driving systems are one method to improve vehicle energy efficiency with the help of vehicle connectivity. In this paper, an eco-driving system is developed that computes a fuel-optimized vehicle trajectory while traversing more than one signalized intersection. The system is designed in a modular and scalable fashion allowing it to be implemented in large networks without significantly increasing the computational complexity. The proposed system utilizes signal phasing and timing (SPaT) data that are communicated to connected vehicles (CVs) together with real-time vehicle dynamics to compute fuel-optimum trajectories. The proposed algorithm is incorporated in the INTEGRATION microscopic traffic assignment and simulation software to conduct a comprehensive sensitivity analysis of various variables, including: system market penetration rates (MPRs), demand levels, phase splits, offsets and traffic signal spacings on the system performance. The analysis shows that at 100\% MPR, fuel consumption can be reduced by as high as 13.8\%. Moreover, higher MPRs and shorter phase lengths result in larger fuel savings. Optimum demand levels and traffic signal spacings exist that maximize the effectiveness of the algorithm. Furthermore, the study demonstrates that the algorithm works less effective when the traffic signal offset is closer to its optimal value. Finally, the study highlights the need for further work to enhance the algorithm to deal with over-saturated traffic conditions.