This paper introduces a new strategy to provide QoS in IP/OBS networks, using Routing with Prioritization Based on Statistics (RPBS). This proposal uses the feedback scheme in optical networks to provide statistical knowledge with the objective of finding a suitable route for reach each destination from a specific source node, with more chance of success. This yields a twofold outcome. First, the losses can be reduced due to the statistics. Second, the delays are also reduced compare with other methods based on feedback scheme. These two improvements allow better QoS provision, supporting class differentiation and more efficient resources utilization. The benefits of this proposal are compared against existent alternatives by simulation. Keywords: OBS, Statistical Routing, WDM, QoS Provision, JET, RPBS