The decision and ability to aggregate packets can have significant impact on the performance of a communication system. The impact can be even more substantial when the system operates under a heavy load. In this paper, we present a queuing model which describes a packet encapsulation and aggregation process. Using this model, we provide analysis of the end-to-end delay of a packet transmitted by the system. The analytical model is verified by a simulation model of the system. We calculate the maximum number of packets in a single frame for which packet aggregation minimizes the average total delay of a packet. It is numerically shown that when the load is high, the higher the variability of the packet service time, the higher the maximum allowed number of packets in the frame should be to achieve the minimum average total packet delay. However, the impact of the variability of the packet service time is insignificant when the system load is moderate or low.