Carrier aggregation is a potential technology for the LTE-Advanced system to support wider bandwidth than the LTE system. This paper analyzes the performance of carrier aggregation under elastic traffic, and compares it to that of a simpler approach for the same purpose, referred to as the independent carrier approach. The queueing behaviors of these two approaches are formulated as one fast versus multiple slow state-dependent Processor Sharing servers, respectively. Both analytical and simulation results show that when there are L component carriers with uniform bandwidth in the system, the performance of the carrier aggregation approach is L times better than that of the independent carrier approach in terms of the average user delay and throughput under the same traffic load.