  In this work, we study the effects of finite buffers on the throughput and
delay of line networks with erasure links. We identify the calculation of
performance parameters such as throughput and delay to be equivalent to
determining the stationary distribution of an irreducible Markov chain. We note
that the number of states in the Markov chain grows exponentially in the size
of the buffers with the exponent scaling linearly with the number of hops in a
line network. We then propose a simplified iterative scheme to approximately
identify the steady-state distribution of the chain by decoupling the chain to
smaller chains. The approximate solution is then used to understand the effect
of buffer sizes on throughput and distribution of packet delay. Further, we
classify nodes based on congestion that yields an intelligent scheme for memory
allocation using the proposed framework. Finally, by simulations we confirm
that our framework yields an accurate prediction of the variation of the
throughput and delay distribution.
