  We analyze a simple network where a source and a receiver are connected by a
line of erasure channels of different reliabilities. Recent prior work has
shown that random linear network coding can achieve the min-cut capacity and
therefore the asymptotic rate is determined by the worst link of the line
network. In this paper we investigate the delay for transmitting a batch of
packets, which is a function of all the erasure probabilities and the number of
packets in the batch. We show a monotonicity result on the delay function and
derive simple expressions which characterize the expected delay behavior of
line networks. Further, we use a martingale bounded differences argument to
show that the actual delay is tightly concentrated around its expectation.
