Increasingly, numerous and various Internet-capable devices are connected in end user networks, such as a home network. Most devices use the combination of TCP and 802.11 DCF as a system platform, but whereas some devices such as a streaming video persistently generate traffic, others such as a motion sensor do so only intermittently with lots of pauses. This study addresses the issue of performance in this heterogeneous traffic wireless LAN environment from the perspective of fairness. First, instantaneous fairness is introduced as a notion to indicate how immediately and how closely a user obtains its fair share, and a new time-based metric is defined as an index. Second, extensive simulation experiments have been made with TCP Reno, Vegas, and Westwood to determine how each TCP congestion control corresponds to the instantaneous fairness. Overall, TCP Vegas yields the best instantaneous fairness because it keeps the queue length shorter than the other TCPs. In the simulations, about 60% of a fair share of the effective user bandwidth is immediately usable in any circumstance. Finally, we introduce two simple strategies for adjusting TCP congestion controls to enhance instantaneous fairness and validate them through simulation experiments.