Data stream processing is an attractive paradigm for analyzing IoT data at the edge of the Internet before transmitting processed results to a cloud. However, the relative scarcity of fog computing resources combined with the workloads' nonstationary properties make it impossible to allocate a static set of resources for each application. We propose Gesscale, a resource auto-scaler which guarantees that a stream processing application maintains a sufficient Maximum Sustainable Throughput to process its incoming data with no undue delay, while not using more resources than strictly necessary. Gesscale derives its decisions about when to rescale and which geo-distributed resource(s) to add or remove on a performance model that gives precise predictions about the future maximum sustainable throughput after reconfiguration. We show that this auto-scaler uses 17% less resources, generates 52% fewer reconfigurations, and processes more input data than baseline auto-scalers based on threshold triggers or a simpler performance model. Index Terms-Stream processing, auto-scaling, fog computing.