  The famous edge flow decomposition theorem of Gallai (1958) states that any
static edge $s$,$d$-flow in a directed graph can be decomposed into a linear
combination of incidence vectors of paths and cycles. In this paper, we study
the decomposition problem for the setting of dynamic edge $s$,$d$-flows
assuming a quite general dynamic flow propagation model. We prove the following
decomposition theorem: For any dynamic edge $s$,$d$-flow with finite support,
there exists a decomposition into a linear combination of $s$,$d$-walk inflows
and circulations, i.e. edge flows that circulate along cycles with zero transit
time. We show that a variant of the classical algorithmic approach of
iteratively subtracting walk inflows from the current dynamic edge flow
converges to a dynamic circulation. The algorithm terminates in finite time, if
there is a lower bound on the minimum edge travel times. We further
characterize those dynamic edge flows which can be decomposed purely into
linear combinations of $s$,$d$-walk inflows.
  The proofs rely on the new concept of parameterized network loadings which
describe how particles of a different walk flow would hypothetically propagate
throughout the network under the fixed travel times induced by the given edge
flow. We show several technical properties of this type of network loading and
as a byproduct we also derive some general results on dynamic flows which could
be of interest outside the context of this paper as well.
