Support of incoming traffic differentiation and Quality of Service (QoS) assurance is very important for the development of high performance packet switches, capable of separating traffic flows. In our previous paper, we proposed the implementation of two buffers at each crosspoint of a crossbar fabric that leads to the Dual Crosspoint Queued (DCQ) switch. Inside DCQ switch, one buffer is used to store the real-time traffic and the other for the non-real-time traffic. We also showed that the static priority algorithms can provide the QoS only for the real-time traffic due to their greedy nature that gives the absolute priority to that type of traffic. In order to overcome this problem, in our paper we propose the DCQ switch with the Largest Weighted Occupancy First scheduling algorithm that provides the desired QoS support for both traffic flows. Detailed analysis of the simulation results confirms the validity of proposed solution.