Queueing Analysis of Continuous Queries for Uncertain Data Streams Over Sliding Windows

With the rapid development of data collection methods and their practical applications, the management of uncertain data streams has drawn wide attention in both academia and industry. System capacity planning and Quality of service (QoS) metrics are two very important problems for data stream management systems (DSMSs) to process streams efficiently due to unpredictable input characteristics and limited memory resource in the system. Motivated by this, in this paper, we explore an effective approach to estimate the memory requirement, data loss ratio, and tuple latency of continuous queries for uncertain data streams over sliding windows in a DSMS. More specifically, we propose a queueing model to address these problems in this paper. We study the average number of tuples, average tuple latency in the queue, and the distribution of the number of tuples and tuple latency in the queue under the Poisson arrival of input data streams in our queueing model. Furthermore, we also determine the maximum capacity of the queueing system based on the data loss ratio. The solutions for the above problems are very important to help researchers design, manage, and optimize a DSMS, including allocating buffer needed for a queue and admitting a continuous uncertain query to the system without violation of the pre-specified QoS requirements.