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Wireless sensor-actuator networks (WSANs) have recently been suggested as an enhancement to the conventional sensor networks. The powerful and mobile actuators can patrol along different routes and communicate with the static sensor nodes. This work is motivated by applications in which the objective is to minimize the data collection time in a stochastic and dynamically changing sensing environment. This is a departure from the previous static and deterministic mobile element scheduling problems. In this paper, we propose PROUD, a probabilistic route design algorithm for wireless sensor-actuator networks. PROUD offers delay-minimized routes for actuators and adapts well to network dynamics and sensors with non-uniform weights. This is achieved through a probabilistic visiting scheme along pre-calculated routes. We present a distributed implementation for route calculation in PROUD and extend it to accommodate actuators with variable speeds. We also propose the Multi-Route Improvement and the Task Exchange algorithms for balancing load among actuators. Simulation results demonstrate that our algorithms can effectively reduce the overall data collection time in wireless sensor-actuator networks. It well adapts to network dynamics and evenly distributes the energy consumption of the actuators.