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We consider a scheduling problem in a wireless network which consists of one base station, N legitimate users and one (or more) eavesdropper(s). The scheduling problem jointly considers the reliability, security and stability of the system, and is to allocate wireless resources to the legitimate users, stabilize the system and maximize the secure transmission rate. Based on the stochastic network optimization framework, the scheduling problem is decomposed to an online optimization problem. A scheduling algorithm and a low computational complexity algorithm that both do not consider power adaptation are proposed, along with a power adaptive one. Extensive simulations are conducted to show the impact of the information arrival rate and the eavesdropper's channel condition on the system performance. These observations provide important insights and guidelines for the design and resource management of …