  We study the store-and-forward packet routing problem for simultaneous
multicasts, in which multiple packets have to be forwarded along given trees as
fast as possible.
  This is a natural generalization of the seminal work of Leighton, Maggs and
Rao, which solved this problem for unicasts, i.e. the case where all trees are
paths. They showed the existence of asymptotically optimal $O(C + D)$-length
schedules, where the congestion $C$ is the maximum number of packets sent over
an edge and the dilation $D$ is the maximum depth of a tree. This improves over
the trivial $O(CD)$ length schedules.
  We prove a lower bound for multicasts, which shows that there do not always
exist schedules of non-trivial length, $o(CD)$. On the positive side, we
construct $O(C+D+\log^2 n)$-length schedules in any $n$-node network. These
schedules are near-optimal, since our lower bound shows that this length cannot
be improved to $O(C+D) + o(\log n)$.
