Existing approaches to the management of streaming positional updates generally assume that all active user requests have equal importance, ignoring the possibility of any priorities concerning delivery of results in mission-critical mobile applications. Query prioritization could be assigned either explicitly after users’ preferences or implicitly by the processing engine itself to better regulate system load. In this work, we specifically examine priority-based evaluation of ranked continuous range queries against locations of moving objects streaming into a central processor. We define a versatile model with alternative scoring functions for deciding evaluation strategies adaptable to the relative importance of queries and the current distribution of objects. We also propose a processing mechanism enhanced with ranked priorities, which exploits shared computation and enables critical requests to receive response more frequently than less demanding ones. A comprehensive experimental study with performance results offers concrete evidence that such a scheme is capable of efficiently handling numerous moving queries of varying priorities and spatial extents with minimal system overhead.