The proliferation of handheld devices with the support of multiple interfaces makes it a common requirement of users to have access to multiple access networks simultaneously in order to obtain increased performance. Aggregating bandwidth of two or more Internet connections makes Internet applications to use the total available bandwidth in order to increase the goodput and reliability with link redundancy. In this paper, a Bandwidth Aggregation System (BAS) along with its implementation is discussed. Moreover a queuing theory based analytical model to derive the performance for aggregating bandwidth using multiple available interfaces for TCP connections is presented. Next, that model has been used to derive an expression for average data transmission rate when BAS is being used. In the end the performance of the model is validated by simulating the BAS and comparing the model predicted results with the experimental results. The comparison shows excellent agreement.