The issue on how to effectively deliver video streaming contents over cloud computing infrastructures is tackled in this study. Basically, quality of service of video streaming is strongly influenced by bandwidth, jitter and data loss problems. A number of intelligent video streaming algorithms are proposed by using different techniques to deal with such issues. This study aims to propose and demonstrate a novel decision making analysis which combines ISO 9126 (international standard for software engineering) and Analytic Hierarchy Process to help experts selecting the best video streaming algorithm for the case of private cloud computing infrastructure. The given case study concluded that Scalable Streaming algorithm is the best algorithm to be implemented for delivering high quality of service of video streaming over the private cloud computing infrastructure.