In this paper, the authors present an enhancement to a category of Adaptive Video Streaming solutions aimed at improving both Quality of Service (QoS) and Quality of Experience (QoE). The specific solution used as baseline for the work is the Smooth Streaming framework from Microsoft. The presented enhancement relates to the rate adaptation scheme used, and suggests applying a stochastic or fixed/unique setting of the rate adjustment intervals rather than the default fixed/equal approach. The main novelty of the paper is the simultaneous study of both network oriented fairness in the QoS domain and perception based fairness from the QoE domain, when introducing the suggested mechanism. The method used for this study is by means of simulations, measurements and numerical optimization.