In this paper, we propose an online-matching-based model to study the assignment problems arising in a wide range of online-matching markets, including online recommendations, ride-hailing platforms, and crowdsourcing markets. It features that each assignment can request a random set of resources and yield a random utility, and the two (cost and utility) can be arbitrarily correlated with each other. We present two linear-programming-based parameterized policies to study the tradeoff between the \emph{competitive ratio} (CR) on the total utilities and the \emph{variance} on the total number of matches (unweighted version). The first one (SAMP) is to sample an edge according to the distribution extracted from the clairvoyant optimal, while the second (ATT) features a time-adaptive attenuation framework that leads to an improvement over the state-of-the-art competitive-ratio result. We also consider the problem under a large-budget assumption and show that SAMP achieves asymptotically optimal performance in terms of competitive ratio.