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Wireless mesh networks have attracted increasing attention and deployment as a high-performance and low-cost solution to last-mile broadband Internet access. Network routing plays a critical role in determining the performance of a wireless mesh network. To study the best mesh network routing strategy which can maximize the network throughput while satisfying the fairness constraints, existing research proposes to formulate the mesh network routing problem as an optimization problem. These works usually make ideal assumptions such as known static traffic input. Whether they could be applied for practical use under the highly dynamic and uncertain traffic in wireless mesh network is still an open issue. The main objective of this paper is to understand the effects of traffic uncertainty in wireless mesh networks and consider these effects in throughput maximization routing. It identifies the appropriate optimization framework that could integrate the statistical user traffic demand model into a tractable throughput maximization problem. The trace-driven simulation study demonstrates that our algorithm can effectively incorporate the traffic demand uncertainty in routing optimization, and outperform the throughput maximization routing which only considers static traffic demand.