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.