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Edge-clouds provide a promising new approach to significantly reduce network operational costs by moving computation closer to the edge. A key challenge in such systems is to decide where and when services should be migrated in response to user mobility and demand variation. The objective is to optimize operational costs while providing rigorous performance guarantees. In this paper, we model this as a sequential decision making Markov Decision Problem (MDP). However, departing from traditional solution methods (such as dynamic programming) that require extensive statistical knowledge and are computationally prohibitive, we develop a novel alternate methodology. First, we establish an interesting decoupling property of the MDP that reduces it to two independent MDPs on disjoint state spaces. Then, using the technique of Lyapunov optimization over renewals, we design an online control algorithm …