Traffic congestion in road networks has been studied as the congestion game in game theory. In the existing work, the road usage by each agent was assumed to be static during the whole time horizon of the agent's travel, as in the classical congestion game. This assumption, however, should be reconsidered because each agent sequentially uses roads composing the route. In this paper, we propose a multi-agent distributed route selection scheme based on a gradient descent method considering the time-dependency among agents' road usage for vehicular networks. The proposed scheme first estimates the time-dependent flow on each road by considering the agents' probabilistic occupation under the first-in-first-out (FIFO) policy. Then, it calculates the optimal route choice probability of each route candidate using the gradient descent method and the estimated time-dependent flow. Each agent finally selects one route according to the optimal route choice probabilities. We first prove that the proposed scheme can exponentially converge to the steady-state at the convergence rate inversely proportional to the product of the number of agents and that of individual route candidates. Through simulations under a grid-like network and a real road network, we show that the proposed scheme can improve the actual travel time by 5.1% and 2.5% compared with the conventional static-flow based approach, respectively. In addition, we demonstrate that the proposed scheme is robust against incomplete information sharing among agents, which would be caused by its low penetration ratio or limited transmission range of wireless communications.