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In this paper, we address how to design the distributed movement strategy for mobile collectors, which can be either physical mobile agents or query/collector packets periodically launched by the sink, to achieve successful data gathering in wireless sensor networks. Formulating the problem as general random walks on a graph composed of sensors, we analyze how many data can be successfully gathered in time under any Markovian movement strategies for mobile collectors moving over a graph (or network), while each sensor is equipped with limited buffer space and data arrival rate to each node is heterogeneous. In particular, from the analysis, we obtain the optimal movement strategy among a class of Markovian strategies so as to minimize the data loss rate over all sensors, and explain how such optimal movement strategy can be made to work in a distributed fashion. We demonstrate that our distributed optimal movement strategy leads to about 2 times smaller loss rate than the simple random walk strategy under diverse scenarios. In particular, our strategy can result in about 50% cost savings for the deployment of multiple collectors to achieve the target data loss rate than the simple random walk.