  Transport processes on spatial networks are representative of a broad class
of real world systems which, rather than being independent, are typically
interdependent. We propose a measure of utility to capture key features that
arise when such systems are coupled together. The coupling is defined in a way
that is not solely topological, relying on both the distribution of sources and
sinks, and the method of route assignment. Using a toy model, we explore
relevant cases by simulation. For certain parameter values, a picture emerges
of two regimes. The first occurs when the flows go from many sources to a small
number of sinks. In this case, network utility is largest when the coupling is
at its maximum and the average shortest path is minimized. The second regime
arises when many sources correspond to many sinks. Here, the optimal coupling
no longer corresponds to the minimum average shortest path, as the congestion
of traffic must also be taken into account. More generally, results indicate
that coupled spatial systems can give rise to behavior that relies subtly on
the interplay between the coupling and randomness in the source-sink
distribution.
