HTTP adaptive streaming (HAS) is a streaming video technique widely used over the Internet. However, it has many drawbacks that degrade its user quality of experience (QoE). Our investigation involves several HAS clients competing for bandwidth inside the same home network. Studies have shown that managing the bandwidth between HAS clients using traffic shaping methods improves the QoE. Additionally, the TCP congestion control algorithm in the HAS server may also impact the QoE because every congestion control variant has its own method to control the congestion window size. Based on previous work, we describe two traffic shaping methods, the Hierarchical Token Bucket shaping Method (HTBM) and the Receive Window Tuning Method (RWTM), as well as four popular congestion control variants: NewReno, Vegas, Illinois, and Cubic. In this paper, our objective is to provide a detailed comparative evaluation of combining these four congestion control variants with these two shaping methods. The main result indicates that Illinois with RWTM offers the best QoE without causing congestion. Results were validated through experimentation and objective QoE analytical criteria.