The Dynamic Traffic Assignment (DTA) is one of the important measures to alleviate urban network traffic congestion. The congestions are usually caused by stochastic traffic demands, which are generally unassignable from time dimension in the real-world but are assumed to be assignable in existing DTA methods (i.e. real-time travel demands). In this paper, a distributed DTA method for preventing urban network traffic congestion caused by stochastic real-time travel demands by improving Multi-Agent Reinforcement Learning (MARL). A team structure, which consists of decision-makers and advisers, is designed to learn parallelly in realistic DTA tasks. To reduce the size of the solution space adaptively, the dynamic critical values advised by adviser agents are adopted as constraints for the strategy space of decision-makers (i.e. main agents). A collaborative heterogeneous-adviser mechanism is designed to avoid deviation of guidance. To enhance the adaptability of DTA to the changeable external environment, the mixed strategy concept is introduced to improve the decision-making process of main agents. The respective mapping mechanisms are designed to define adaptive learning rates to improve the sensitivity of MARL. The Sioux Falls (SF) network is established as a test platform via a Dynamic Network Loading (DNL). The effectiveness of the suggested DTA method is assessed through numerical simulations SF network. Under the influence of the scenario with stochastic real-time travel demands, the results show that the proposed method outperforms in terms of the throughput of the network and the individual average travel time among the overall network. Additionally, the ability of the proposed method in response to the external environment rapidly has also been demonstrated. Adopting the suggested method can improve the state of the art to assign stochastic real-time travel demands dynamically and to avoid potential traffic congestion fundamentally. INDEX TERMS dynamic traffic assignment, intelligent transportation system, multi-agent system, reinforcement learning, multi-agent reinforcement learning, numerical simulation.