In automated logistics systems, travel time uncertainty can severely affect automated guided vehicle (AGV) conflict and path planning. Insight is required into how travel time uncertainty affects catch-up conflict, the main AGV conflict in one-way road networks. Under normal circumstances, the probability formula for catch-up conflict is deduced based on an analysis of AGV catch-up conflict. The vertex, monotonicity, and symmetry of catch-up conflict probabilities are developed, for symmetrical AGV travel time distribution densities. A dynamic adjustment method based on conflict probability for AGVs is designed. The probability features of catch-up conflicts and the performance of the associated dynamic adjustment are simulated and validated for AGVs at an automated container terminal. The simulation results show that the impact analysis of travel time uncertainty on AGV catch-up conflict is correct, and the dynamic adjustment is effective.