A detailed mathematical model for the fission yeast mitotic cycle is developed based on positive and negative feedback loops by which Cdc13yCdc2 kinase activates and inactivates itself. Positive feedbacks are created by Cdc13yCdc2-dependent phosphorylation of specific substrates: inactivating its negative regulators (Rum1, Ste9 and Wee1yMik1) and activating its positive regulator (Cdc25). A slow negative feedback loop is turned on during mitosis by activation of Slp1yanaphase-promoting complex (APC), which indirectly re-activates the negative regulators, leading to a drop in Cdc13yCdc2 activity and exit from mitosis. The model explains how fission yeast cells can exit mitosis in the absence of Ste9 (Cdc13 degradation) and Rum1 (an inhibitor of Cdc13yCdc2). We also show that, if the positive feedback loops accelerating the G2yM transition (through Wee1 and Cdc25) are weak, then cells can reset back to G2 from early stages of mitosis by premature activation of the negative feedback loop. This resetting can happen more than once, resulting in a quantized distribution of cycle times, as observed experimentally in wee12 cdc25D mutant cells. Our quantitative description of these quantized cycles demonstrates the utility of mathematical modeling, because these cycles cannot be understood by intuitive arguments alone.