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A significant amount of wireless traffic is expected to be carried in the Internet, and wireless connections need to share the network resources with wired connections. However, in a wireless network environment, TCP, one of the most important transport protocols of TCP/IP, suffers from significant throughput degradation due to the lossy characteristics of a wireless link. Therefore, in order to design the next generation mobile networks, it is necessary to know how much the wireless connection suffers from the degradation in comparison to the wired connection. We discuss the fairness issue between TCP connections over wireless and wired links, and theoretically analyze throughput fairness between TCP over a wireless link with ARQ (automatic repeat request) based link layer error recovery and TCP over an error-free wired link. We validate our analysis by comparing numerical results obtained from the analysis with computer simulation ones.