State-of-the-art distributed stream processing systems such as Apache Flink and Storm have recently included checkpointing to provide fault-tolerance for stateful applications. This is a necessary eventuality as these systems head into the Exascale regime, and is evidently more efficient than replication as state size grows. However current systems use a nominal value for the checkpoint interval, indicative of assuming roughly 1 failure every 19 days, that does not take into account the salient aspects of the checkpoint process, nor the system scale, which can readily lead to inefficient system operation. To address this shortcoming, we provide a rigorous derivation of utilization -- the fraction of total time available for the system to do useful work -- that incorporates checkpoint interval, failure rate, checkpoint cost, failure detection and restart cost, depth of the system topology and message delay. Our model yields an elegant expression for utilization and provides an optimal checkpoint interval given these parameters, interestingly showing it to be dependent only on checkpoint cost and failure rate. We confirm the accuracy and efficacy of our model through experiments with Apache Flink, where we obtain improvements in system utilization for every case, especially as the system size increases. Our model provides a solid theoretical basis for the analysis and optimization of more elaborate checkpointing approaches.