Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.