  We develop techniques to analyse the statistics of completion times of
non-deterministic elements in quantum entanglement generation, and how they
affect the overall performance as measured by the secret key rate. By
considering such processes as Markov chains, we show how to obtain exact
expressions for the probability distributions over the number of errors that a
network acquires, as well as the distribution of entanglement establishment
times. We show how results from complex analysis can be used to analyse Markov
matrices to extract information with a lower computational complexity than
previous methods. We apply these techniques to the Innsbruck quantum repeater
protocol, and find that consideration of the effect of statistical fluctuations
tightens bounds on the secret key rate by 3 orders of magnitude. We also use
the theory of order statistics to derive tighter bounds on the minimum quantum
memory lifetimes that are required in order to communicate securely.
