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Consider a team of agents in the plane searching for and visiting targetpoints that appear in a bounded environment according to a stochastic renewalprocess with a known absolutely continuous spatial distribution. Agents mustdetect targets with limited-range onboard sensors. It is desired to minimizethe expected waiting time between the appearance of a target point, and theinstant it is visited. When the sensing radius is small, the system time isdominated by time spent searching, and it is shown that the optimal policyrequires the agents to search a region at a relative frequency proportional tothe square root of its renewal rate. On the other hand, when targets appearfrequently, 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 regionat a relative frequency proportional to the cube root of its renewal rate.Furthermore, the presented algorithms in this case recover the optimalperformance achieved by agents with full information of the environment.Simulation results verify the theoretical performance of the algorithms.

Optimal Foraging of Renewable Resources