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Mobile Edge Computing may become a prevalent platform to support applications where mobile devices have limited compute, storage, energy and/or data privacy concerns. In this paper, we study the efficient provisioning and man- agement of compute resources in the Edge-to-Cloud continuum for different types of real-time applications with timeliness requirements depending on application-level update rates and communication/compute delays. We begin by introducing a highly stylized network model allowing us to study the salient features of this problem including its sensitivity to compute vs. communication costs, application requirements, and traffic load variability. We then propose an online decentralized service placement algorithm, based on estimating network delays and adapting application update rates, which achieves high service availability. Our results exhibit how placement can be optimized and how a load-balancing strategy c