We consider networked control systems where nodes (sensors, actuators, and controller) are connected via a communication network that allows only one user to transmit at a given time. We tackle the scheduling problem of deciding which node should access the network at each transmission time so as to optimize a quadratic performance objective. Using the framework of dynamic programming, we propose a rollout strategy by which the node elected to transmit at each step is the one that leads to optimal performance over a lookahead horizon assuming that from then on nodes transmit in a periodic order. The proposed strategy leads to a protocol in which a conic state partition determines which node transmits at each step and which can outperform any given periodic protocol. Moreover, we show that some of the protocols previously proposed in the literature, such as the Maximum Error First and the dynamic protocols, can be viewed as rollout strategies for a certain dynamic programming problem. The advantages of using rollout strategies are illustrated by a numerical example.