Last decade witnessed the explosive growth in mobile devices and their traffic demand, and hence the significant increase in the energy cost of the cellular service providers. One major component of energy expenditure comes from the operation of base stations. How to reduce energy cost of base stations while satisfying users’ soaring demands has become an imperative yet challenging problem. In this dissertation, we investigate the minimization of the long-term time-averaged expected energy cost while guaranteeing network strong stability. Specifically, considering flow routing, link scheduling, and energy constraints, we formulate a time-coupling stochastic Mixed-Integer Non-Linear Programming (MINLP) problem, which is prohibitively expensive to solve. We reformulate the problem by employing Lyapunov optimization theory and develop a decomposition based algorithm which ensures network strong stability. We obtain the bounds on the optimal result of the original problem and demonstrate the tightness of the bounds and the efficacy of the proposed scheme.