  In a network, a node is said to incur a delay if its encoding of each
transmitted symbol involves only its received symbols obtained before the time
slot in which the transmitted symbol is sent (hence the transmitted symbol sent
in a time slot cannot depend on the received symbol obtained in the same time
slot). A node is said to incur no delay if its received symbol obtained in a
time slot is available for encoding its transmitted symbol sent in the same
time slot. Under the classical model, every node in a discrete memoryless
network (DMN) incurs a unit delay, and the capacity region of the DMN satisfies
the well-known cut-set outer bound. In this paper, we propose a generalized
model for the DMN where some nodes may incur no delay. Under our generalized
model, we obtain a new cut-set outer bound, which is proved to be tight for
some two-node DMN and is shown to subsume an existing cut-set bound for the
causal relay network. In addition, we establish under the generalized model
another cut-set outer bound on the positive-delay region -- the set of
achievable rate tuples under the constraint that every node incurs a delay. We
use the cut-set bound on the positive-delay region to show that for some
two-node DMN under the generalized model, the positive-delay region is strictly
smaller than the capacity region.
