The emergence of new applications brings multi-class traffic with diverse quality of service (QoS) demands in wide area networks (WANs), which motivates the research in traffic engineering (TE). In recent years, novel centralized TE schemes have employed heuristic or machine-learning techniques to orchestrate resources in closed systems, such as datacenter networks. However, these schemes suffer long delivery delay and high control overhead when applied to general WANs. Semi-centralized TE schemes have been proposed to address these drawbacks, providing lower delay and control overhead. Despite this, they suffer performance degradation dealing with volatile traffic. To provide low-delay service and keep high network utility, we propose an asynchronous multi-class traffic management scheme, AMTM. We first establish an asynchronous TE paradigm, in which distributed nodes instantly make traffic control decisions based on link prices. To manage varying traffic and control delivery time, we propose state-based iteration strategies of link pricing under different scenarios and investigate their convergence. Furthermore, we present a system design and corresponding algorithms. Simulation results indicate that AMTM outperforms existing schemes in terms of both delay reduction and scalability improvement. In addition, AMTM outperforms the semi-centralized scheme with 12-20$\%$ more network utility and achieves 2-7$\%$ less network utility compared to the theoretical optimum.
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