The large scale of current and next-generation massively parallel processing (MPP) systems presents significant challenges related to fault tolerance. For applications that perform periodic checkpointing, the choice of the checkpoint interval, the period between checkpoints, can have a significant impact on the execution time of the application and the number of checkpoint I/O operations performed by the application. These two metrics determine the frequency of checkpoint I/O operations performed by the application, and thereby, the contribution of the checkpoint operations to the I/O bandwidth demand made by the application. In a computing environment where there are concurrent applications competing for access to the network and storage resources, the I/O demand of each application is a crucial factor in determining the throughput of the system. Thus, in order to achieve a good overall system throughput, it is important for the application programmer to choose a checkpoint interval that balances the two opposing metrics - the number of checkpoint I/O operations and the application execution time. Finding the optimal checkpoint interval that minimizes the wall clock execution time, has been a subject of research over the last decade. In this paper, we present a simple, elegant, and accurate analytical model of a complementary performance metric - the aggregate number of checkpoint I/O operations. We model this and present the optimal checkpoint interval that minimizes the total number of checkpoint I/O operations. We present extensive simulation studies that validate our analytical model. Insights provided by this model, combined with existing models for wall clock execution time, facilitate application programmers in making a well informed choice of checkpoint interval leading to an appropriate trade off between execution time and number of checkpoint I/O operations. We illustrate the existence of such propitious checkpoint intervals using parameters of four MPP systems, SNL's Red Storm, ORNL's Jaguar, LLNL's Blue Gene/L (BG/L), and a theoretical Petaflop system.