The concept of fog computing is centered around providing computation resources at the edge of network, thereby reducing the latency and improving the quality of service. However, it is still desirable to investigate how and where at the edge of the network the computation capacity should be provisioned. To this end, we propose a hierarchical capacity provisioning scheme. In particular, we consider a two-tier network architecture consisting of shallow and deep cloudlets and explore the benefits of hierarchical capacity based on queueing analysis. Moreover, we explore two different network scenarios in which the network delay between the two tiers is negligible as well as the case that the deep cloudlet is located somewhere deeper in the network and thus the delay is significant. More importantly, we model the first network delay scenario with bufferless shallow cloudlets as well as the second scenario with finite-size buffer shallow cloudlets, and formulate an optimization problem for each model. We also use stochastic ordering to solve the optimization problem formulated for the first model and an upper bound based technique is proposed for the second model. The performance of the proposed scheme is evaluated via simulations in which we show the accuracy of the proposed upper bound technique as well as the queue length estimation approach for both randomly generated input and real trace data.
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