Maintaining consistent results of continuous queries under diverse window specifications

Continuous queries applied over nonterminating data streams usually specify windows in order to obtain an evolving–yet restricted–set of tuples and thus provide timely and incremental results. Although sliding windows get frequently employed in many user requests, additional types like partitioned or landmark windows are also available in stream processing engines. In this paper, we set out to study the existence of monotonic-related semantics for a rich set of windowing constructs in order to facilitate a more efficient maintenance of their changing contents. After laying out a formal foundation for expressing windowed queries, we investigate update patterns observed in most common window variants as well as their impact on adaptations of typical operators (like windowed join, union or aggregation), thus offering more insight towards design and implementation of stream processing mechanisms. Furthermore, we identify syntactic equivalences in algebraic expressions involving windows, to the potential benefit of query optimizations. Finally, this framework is validated for several windowed operations against streaming datasets with simulations at diverse arrival rates and window specifications, providing concrete evidence of its significance.