Why being patient or why not?

Our subject is a wolf. He is thrown into a world comprised of sites. There are two kinds of sites: easy sites, where a rabbit is coming every T1 hours, and hard sites, where a rabbit is coming every T2 hours, T2>T1. The wolf knows that the density of easy sites is p, 0<p<1. How long should the wolf wait at one site before he decides to move around? Some extreme cases: if T2=infinite, the wolf should wait no longer than T1, and if T2=T1, he should probably just keep waiting. This decision also clearly depends on the value of p. For example, if p is 0, the wolf is better off just waiting. Note that the same strategy doesn't apply to p=1. This can explain why different animals have different behavioral patterns in terms of patience; it is an adaptation to their individual environments.

Some preliminary results show that, after waiting time of T1, the wolf is better off moving if p>T1/(T2-T1), and he should keep waiting otherwise.