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The transmission control protocol (TCP) is widely used in wired and wireless networks. It provides reliable transport services between end-to-end hosts. Since TCP performance affects the overall network performance, several analytical models were proposed to describe the steady-state throughput of bulk transfer TCP flows (i.e., a flow with large amount of data to send, such as FTP transfers). However, most TCP flows in the Internet world are short-lived to see few losses and they cannot reach the steady-state, consequently their performance is determined by the startup effects such as the connection establishment and the slow start mechanisms. Surprisingly, all of the previous models did not investigate the heterogeneity of wireless networks which is considered the most important issue in wired-cum-wireless networks. The heterogeneity is shown by different characteristics and different segment loss probability for various types of wireless networks such as IEEE 802.11 WLAN and 3G cellular network. Moreover, wireless TCP flows are much shorter than wired flows due to the time varying characteristics of wireless networks. In this research, a recursive and analytical model is developed and used to determine the performance of TCP in heterogeneous wired-cum-wireless networks in terms of average completion time for the short-lived TCP flows is proposed. The proposed model focuses on heterogeneous wireless networks. The proposed model is based on the knowledge of average dropping probability, the average roundtrip time and the flow size both wired and wireless links. The simulation results are very much the same as the values obtained from the analytical model.