  Consider a system of $K$ particles moving on the vertex set of a finite
connected graph with at most one particle per vertex. If there is one, the
particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location
uniformly at random at rate $\rho_x$, and jumps to that vertex if and only if
it is empty. Using standard probability techniques, we identify the set of
invariant measures of this process to study the occupation time at each vertex.
Our main result shows that, though the occupation time at vertex $x$ increases
with $\hbox{deg} (x) / \rho_x$, the ratio of the occupation times at two
different vertices converges monotonically to one as the number of particles
increases to the number of vertices. The occupation times are also computed
explicitly for simple examples of finite connected graphs: the star and the
path.
