In this paper, we study an extension of atomic routing games for multi-class communication networks with quality of service requirements, which can be formulated as a network management scheme. Atomic routing games are non-cooperative games with multiple selfish players, where each player has to choose a path in a given graph to route his traffic, and then pays the corresponding cost. We develop a mixed-integer nonlinear programming model for the network management scheme in this class-based communication network. The analysis of this work offers appropriate resource allocation and a routing database identifying suitable end-to-end paths upon each connection request.