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TCP does not perform well in a connection that includes a lossy wireless link. Techniques intended to improve the performance of TCP for such connections can be grouped into three categories: end-to-end, link layer and split-connection approaches. Some simulations and experimental results indicate that split-connection protocols yield better performance than the other two approaches. Although analytical modeling of the end-to-end and link-layer approaches has been presented, no comparable performance analysis for split-connection protocols has been reported previously. In this paper, a stochastic model is developed and used to analyze the performance of a class of split-connection protocols which deploy TCP on the wire-line network and a light-weight transport protocol on the wireless final hop. The final hop is provided by a digital TDMA cellular system. The condition of heavy source traffic to the wireless terminal is considered. The model relates the throughput and some useful auxiliary performance measures to key system parameters such as propagation delays, the base-station buffer size, the ARQ protocol and channel-error process of the wireless link. The usefulness of the analysis is illustrated by its application to the problem of sizing the TCP receiving buffer in a base station.