  We consider diffusion-limited annihilating systems with mobile $A$-particles
and stationary $B$-particles placed throughout a graph. Mutual annihilation
occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in
discrete time, are also referred to as parking processes. We show for a broad
family of graphs and random walk kernels that augmenting either the size or
variability of the initial placements of particles increases the total
occupation time by $A$-particles of a given subset of the graph. A corollary is
that the same phenomenon occurs with the total lifespan of all particles in
internal diffusion-limited aggregation.
