  Brane inflation in superstring theory ends when branes collide, initiating
the hot big bang. Cosmic superstrings are produced during the brane collision.
The cosmic superstrings produced in a D3-brane-antibrane inflationary scenario
have a spectrum: $(p,q)$ bound states of $p$ fundamental (F) strings and $q$
D-strings, where $p$ and $q$ are coprime. By extending the velocity-dependent
one-scale network evolution equations for abelian Higgs cosmic strings to allow
a spectrum of string tensions, we construct a coupled (infinite) set of
equations for strings that interact through binding and self-interactions. We
apply this model to a network of $(p,q)$ superstrings. Our numerical solutions
show that $(p,q)$ networks rapidly approach a stable scaling solution. We also
extract the relative densities of each string type from our solutions.
Typically, only a small number of the lowest tension states are populated
substantially once scaling is reached. The model we study also has an
interesting new feature: the energy released in $(p,q)$ string binding is by
itself adequate to allow the network to reach scaling. This result suggests
that the scaling solution is robust. To demonstrate that this result is not
trivial, we show that choosing a different form for string interactions can
lead to network frustration.
