  Explicit expressions for arrival times of particles moving in a
one-dimensional Zero-Range Process (ZRP) are computed. Particles are fed into
the ZRP from an injection site and can also evaporate from anywhere in the
interior of the ZRP. Two dynamics are considered; bulk dynamics, where particle
hopping and decay is proportional to the numqber of particles at each site, and
surface dynamics, where only the top particle at each site can hop or
evaporate. We find exact solutions in the bulk dynamics case and for a
single-site ZRP obeying surface dynamics. For a multisite ZRP obeying surface
dynamics, we compare simulations with approximations obtained from the
steady-state limit, where mean interarrival times for both models are
equivalent. Our results highlight the competition between injection and
evaporation on the arrival times of particles to an absorbing site.
