In this paper we present an innovative game theoretic non-cooperative model for the quality of service (QoS) routing in communication networks implementing a differentiated service model for the QoS support. The proposed model allows us to solve a joint problem of non-cooperative QoS routing and dynamic capacity allocation over a network of parallel links. This problem is solved by playing a Nash game taking place among players belonging to two categories: (i) the category of individual users, whose objectives are to ship their macroflows from the source node to the destination node, by suitably splitting them over the parallel links, and (ii) the category of capacity players, whose task is to partition and to assign to the classes of traffic upon which the macroflows are mapped, the dynamic portion of capacity over each link. One of the main innovative aspects of our model is that the allocation of the dynamic portion of capacity to each class of traffic over each link is realised during the actual operation of the network, i.e. in conjunction with the QoS routing. Extensive simulation results validate the proposed model, show some of its interesting properties and highlight the remarkable performance enhancements that it achieves with respect to the other results present in the literature.