Studying recommender systems under streaming scenarios has become increasingly important because real-world applications produce data continuously and rapidly. However, most existing recommender systems today are designed in the context of an offline setting. Compared with the traditional recommender systems, large-volume and high-velocity are posing severe challenges for streaming recommender systems. In this paper, we investigate the problem of streaming recommendations being subject to higher input rates than they can immediately process with their available system resources (i.e., CPU and memory). In particular, we provide a principled framework called as SPMF (Stream-centered Probabilistic Matrix Factorization model), based on BPR (Bayesian Personalized Ranking) optimization framework, for performing efficient ranking based recommendations in stream settings. Experiments on three real-world datasets illustrate the superiority of SPMF in online recommendations.