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The empty vehicle redistribution (EVR) problem is to decide when and where to move empty vehicles in a Personal Rapid Transit or taxi system. These decisions are made in real time by an EVR algorithm. A reactive EVR algorithm moves empty vehicles only in response to known requests; in contrast, a proactive EVR algorithm moves empty vehicles in anticipation of future requests. This paper describes two new proactive EVR algorithms, called sampling and voting (SV) and dynamic transportation problem (DTP), that move empty vehicles proactively based on demand estimates from historical data. It also develops methods for assessing the performance of EVR algorithms absolutely in terms of both throughput and passenger waiting times. In simulation tests, the proposed algorithms provide lower passenger waiting times than other algorithms in the literature, and proactive movement of empty vehicles significantly reduces waiting times, usually with a modest increase in empty vehicle travel. [ABSTRACT FROM PUBLISHER]