This paper introduces a formal method to model the level of de-mand on control when executing cognitive processes. The costof cognitive control is parsed into an intensity cost which en-capsulates how much additional input information is requiredso as to get the specified response, and an interaction costwhich encapsulates the level of interference between individ-ual processes in a network. We develop a formal relationshipbetween the probability of successful execution of desired pro-cesses and the control signals (additive control biases). Thisrelationship is also used to specify optimal control policies toachieve a desired probability of activation for processes. Weobserve that there are boundary cases when finding such con-trol policies which leads us to introduce the interaction cost.We show that the interaction cost is influenced by the relativestrengths of individual processes, as well as the directionalityof the underlying competition between processes.