We consider the virtual circuit routing problem in the stochastic model with uniformly random arrival requests. In the problem, a graph is given and requests arrive in a uniform random order.Each request is specified by its connectivity demand and the load of a request on an edge is a randomvariable with known distribution. The objective is to satisfy the connectivity request demands whilemaintaining the expected congestion (the maximum edge load) of the underlying network as smallas possible.Despite a large literature on congestion minimization in the deterministic model, not muchis known in the stochastic model even in the offline setting. In this paper, we present anO(log n/ log log n)-competitive algorithm when optimal routing is sufficiently congested. This ratiomatches to the lower bound Ω(log n/ log log n) (assuming some reasonable complexity assumption)in the offline setting. Additionally, we show that, restricting on the offline setting with deterministicloads, our algorithm yields the tight approximation ratio of Θ(log n/ log log n). The algorithm isessentially greedy (without solving LP/rounding) and the simplicity makes it practically appealing.