  In this thesis, we present a flexible framework for specifying and
constructing operads which are suited to reasoning about network construction.
The data used to present these operads is called a \emph{network model}, a
monoidal variant of Joyal's combinatorial species. The construction of the
operad required that we develop a monoidal lift of the Grothendieck
construction. We then demonstrate how concepts like priority and dependency can
be represented in this framework. For the former, we generalize Green's graph
products of groups to the context of universal algebra. For the latter, we
examine the emergence of monoidal fibrations from the presence of catalysts in
Petri nets.
