  Consider a team of agents in the plane searching for and visiting target
points that appear in a bounded environment according to a stochastic renewal
process with a known absolutely continuous spatial distribution. Agents must
detect targets with limited-range onboard sensors. It is desired to minimize
the expected waiting time between the appearance of a target point, and the
instant it is visited. When the sensing radius is small, the system time is
dominated by time spent searching, and it is shown that the optimal policy
requires the agents to search a region at a relative frequency proportional to
the square root of its renewal rate. On the other hand, when targets appear
frequently, the system time is dominated by time spent servicing known targets,
and it is shown that the optimal policy requires the agents to service a region
at a relative frequency proportional to the cube root of its renewal rate.
Furthermore, the presented algorithms in this case recover the optimal
performance achieved by agents with full information of the environment.
Simulation results verify the theoretical performance of the algorithms.
