Queueing Analysis of SPJ Queries over Continuous Data Streams

Currently, considerable body of work exists on stream data processing. Research on data streams varies from algorithms for computing various operators on streams to the design of architectures and implementation of systems for large scale stream processing. Most of the work has focused on the use of queues with traditional query processing operators to handle unpredictable, real-time processing of stream data. To the best of our knowledge, there is little or no work on the queueing analysis of continuous, real-time data and its processing using relational operators/queries. In this paper, we present an analysis based on the queueing theory to study the behavior of stream data in a query processing system. Our approach enables us to compute the mean number of tuples, the variance of the number of tuples, and the mean as well as the variance of the waiting time of tuples in the system. Furthermore, this approach establishes a way to find the probability distribution functions of both the number of tuples and the waiting time of tuples in the system. Finally, we have designed and implemented a number of experiments to demonstrate the accuracy and effectiveness of our analysis. We believe that the results of this paper are extremely useful for the design of stream processing systems and for the understanding of the behavior of stream data.