Operating distributed cloudlets at optimal cost is nontrivial when facing not only the dynamic and unpredictable resource prices and user requests, but also the low efficiency of today's immature cloudlet infrastructures. We propose to control cloudlet networks at multiple granularities: fine-grained control of servers inside cloudlets and coarse-grained control of cloudlets themselves. We model this problem as a mixed-integer nonlinear program with the switching cost over time. To solve this problem online, we firstly linearize, "regularize", and decouple it into a series of one-shot subproblems that we solve at each corresponding time slot, and afterwards we design an iterative, dependent rounding framework using our proposed randomized pairwise rounding algorithm to convert the fractional control decisions into the integral ones at each time slot. Via rigorous theoretical analysis, we exhibit our approach's performance guarantee in terms of the competitive ratio and the multiplicative integrality gap towards the offline optimal integral decisions. Extensive evaluations with real-world data confirm the empirical superiority of our approach over the single granularity server control and the state-of-the-art algorithms.