Providing minimum throughput guarantees is one of the goals for radio resource allocation schemes. It is difficult to provide these guarantees without defining violation probability due to limited power budget and rapidly changing conditions of the wireless channel. For every practical scheduling scheme, there is a feasibility region defined by the minimum guaranteed throughput and the corresponding probability that the users fail to get the guaranteed throughput (violation probability). In this work, we focus on minimizing the violation probability specifically in the small probability region. We compare our results with major schedulers available in literature and show that our scheme outperforms them in the small violation probability region.