This paper addresses the issues of rate control and routing for cloud data center networks. Based on the theory of the supply–demand equilibrium, we propose a fixed point model for formulating cloud network equilibrium problems in which the equilibrium conditions are given by nonlinear equations. We show that the network equilibrium point is the optimal solution of a nonlinear programming problem by utilizing the tools of the variational inequality and convex optimization. The augmented Lagrangian multiplier algorithm is used to solve the nonlinear programming problem for computing the network equilibrium point. Further consideration is given to the equilibrium problems of a cloud network with multirate multicast sessions. We evaluate our approach on some random networks with unicast and multicast sessions, and the results show the effectiveness of our approach in finding the optimal equilibrium rates. We further evaluate the performance of our approach through cloud data center network simulation under various parameter settings, and the results show that the performance of our algorithm can be tuned and improved by choosing appropriate parameter values. Copyright © 2013 John Wiley & Sons, Ltd.