On-orbit satellite servicing is critical to maximizing space utilization and sustainability and is of growing interest for commercial, civil, and defense applications. Reliance on astronauts or anchored robotic arms for the servicing of next-generation large, complex space structures operating beyond Low Earth Orbit is impractical. Substantial literature has investigated the mission design and analysis of robotic servicing missions that utilize a single servicing satellite to approach and service a single target satellite. This motivates the present research to investigate a fleet of servicing satellites performing several operations for a large, central space structure. This research leverages a distributed control approach, implemented using the Horizon Simulation Framework (HSF), to develop a tool capable of integrated mission modeling and task scheduling for a servicing satellite fleet. HSF is a modeling and simulation framework for verification of system level requirements with an emphasis on state representations, modularity, and event scheduling. HSF consists of two major modules: the main scheduling algorithm and the system model. The distributed control architecture allocates processing and decision making for this multi-agent cooperative control problem across multiple subsystem models and the main HSF scheduling algorithm itself. Models were implemented with a special emphasis on the dynamics, control, trajectory constraints, and trajectory optimization for the servicing satellite fleet. The integrated mission modeling and scheduling tool was applied to a sample scenario in which a fleet of 3 servicing assets is tasked with performing 12 servicing activities for a large satellite in Geostationary Orbit. The tool was able to successfully determine a schedule in which all 12 servicing activities were completed in under 32 hours, subject to the fuel and trajectory constraints of the servicing assets.