Data aggregation, which is the process of summarizing a large amount of data, is an effective method for saving limited communication resources, such as radio frequency and sensor-node energy. Packet aggregation in wireless LAN and sensed-data aggregation in wireless sensor networks are typical examples. We propose and analyze two queueing models of fundamental statistical data aggregation schemes: constant interval and constant aggregation number. We represent each aggregation scheme by a tandem queueing network model with a gate at the aggregation process and a single server queue at a transmission process. We analytically derive the stationary distribution and Laplace-Stieltjes transform of the system time for each aggregation and transmission process and of the total system time. We then numerically evaluate the stationary mean system time characteristics and clarify that each model has an optimal aggregation parameter (i.e., an optimal aggregation interval or optimal aggregation number), that minimizes the mean total system time. In addition, we derive the explicit optimal aggregation parameter for a D/M/1 transmission model with each aggregation scheme and clarify that it provides accurate approximation of that of each aggregation model. The optimal aggregation interval was determined by the transmission rate alone, while the optimal aggregation number was determined by the arrival and transmission rates alone with explicitly derived proportional constants. These results can provide a theoretical basis and a guideline for designing aggregation devices, such as IoT gateways.

The spread of the Internet of Things (IoT) has led to the generation of large amounts of data, requiring massive communication, computing, and storage resources. Cloud computing plays an important role in realizing most IoT applications classified as massive machine type communication and cyber-physical control applications in vertical domains. To handle the increasing amount of IoT data, it is important to reduce the traffic concentrated in the cloud by distributing the computing and storage resources to the network edge side and to suppress the latency of the IoT applications. In this paper, we first present a recent literature review on fog/edge computing and data aggregation as representative traffic reduction technologies for efficiently utilizing communication, computing, and storage resources in IoT systems, and then focus on data aggregation control minimizing the latency in an IoT gateway. We then present a unified modeling for statistical and nonstatistical data aggregation and analyze its latency. We analytically derive the Laplace-Stieltjes transform and average of the stationary distribution of the latency and approximate the average latency; we subsequently apply it to an adaptive aggregation number control for the time-variant data arrival. The transient traffic characteristics, that is, the absorption of traffic fluctuations realizing a stable optimal latency, were clarified through a simulation with a time-variant Poisson input and non-Poisson inputs, such as a Beta input, which is a typical IoT traffic model.