This paper studies the control of distributed storage networks with guarantees of constraints satisfaction and asymptotic stability. We consider two problems: network capacity maximization and network balancing. In the first part of the paper we describe the two problems, highlight their importance in a wide number of engineering applications, and compare them by analyzing the properties of their solutions. In the second part we present algorithms for solving both problems by using a convex one-step model predictive controller (MPC) which guarantees persistent state and flow constraints satisfaction. We present simple conditions which link the network topology, the MPC weights and the asymptotic stability of the closed-loop system. A numerical example illustrates the effectiveness of the proposed approach. (C) 2013 Elsevier Ltd. All rights reserved.