Cytokinesis in fission yeast is controlled by a signal transduction pathway called the Septation Initiation Network (SIN). From a dynamical point of view the most interesting questions about the regulation of fission yeast cytokinesis are: how do wild type cells ensure that septation is initiated only once per cycle? Why does the control system stay in a continuously septating state in some mutant strains? And how is it that the SIN remains active when cytokinesis fails? To answer these questions we construct a simplified mathematical model of the SIN and graft this regulatory module onto our previous model of cyclin-dependent kinase (Cdk) dynamics in fission yeast cells. The SIN is both activated and inhibited by mitotic Cdk/cyclin complexes. As a consequence of this dual regulation, the SIN gets activated only once at the end of mitosis, when Cdk activity drops. The mathematical model describes the timing of septation not only in wild type cells but also in mutants where components of the SIN are knocked out. The model predicts phenotypes of some uncharacterized mutant cells and shows how a cytokinesis checkpoint can stop the cell cycle if septation fails.