Before revision:  We study these models under various assumptions on the patience (number of given probes)of the online vertices, and whether edges or offline vertices are weighted in determining the stochastic reward.
After revision:  We establish competitive bounds in these settings, all of which generalize the standard non-stochastic setting when edges do not need to be probed (i.e., exist with certainty). All of our competitive ratios hold for arbitrary edge probabilities and patience constraints: (1) A 1-1/e ratio when the stochastic graph is known, offline vertices are weighted in determining the stochastic reward.