  Quantum repeater chains will form the backbone of future quantum networks
that distribute entanglement between network nodes. Therefore, it is important
to understand the entanglement distribution performance of quantum repeater
chains, especially their throughput and latency. By using Markov chains to
model the stochastic dynamics in quantum repeater chains, we offer analytical
estimations for long-run throughput and on-demand latency of continuous
entanglement distribution. We first study single-link entanglement generation
using general multiheralded protocols. We then model entanglement distribution
with entanglement swapping over two links, using either a single- or a
double-heralded entanglement generation protocol. We also demonstrate how the
two-link results offer insights into the performance of general $2^k$-link
nested repeater chains. Our results enrich the quantitative understanding of
quantum repeater network performance, especially the dependence on system
parameters. The analytical formulae themselves are valuable reference resources
for the quantum networking community. They can serve as benchmarks for quantum
network simulation validation or as examples of quantum network dynamics
modeling using the Markov chain formalism.
