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Unmanned Aerial Vehicles (UAVs) or drones are increasingly used for urban applications like traffic monitoring and construction surveys. Autonomous navigation allows drones to visit waypoints and accomplish activities as part of their mission. A common activity is to hover and observe a location using on-board cameras. Advances in Deep Neural Networks (DNNs) allow such videos to be analyzed for automated decision making. UAVs also host edge computing capability for on-board inferencing by such DNNs. To this end, for a fleet of drones, we propose a novel Mission Scheduling Problem (MSP) that co-schedules the flight routes to visit and record video at waypoints, and their subsequent on-board edge analytics. The proposed schedule maximizes the utility from the activities while meeting activity deadlines as well as energy and computing constraints. We first prove that MSP is NP-hard and then optimally solve it by formulating a mixed integer linear programming (MILP) problem. Next, we design two efficient heuristic algorithms, JSC and VRC, that provide fast sub-optimal solutions. Evaluation of these three schedulers using real drone traces demonstrate utility–runtime trade-offs under diverse workloads.