Optimal Blind and Adaptive Fog Orchestration under Local Processor Sharing

This paper studies the tradeoff between running cost and processing delay in order to optimally orchestrate multiple fog applications. Fog applications process batches of objects' data along chains of containerised microservice modules, which can run either for free on a local fog server or run in cloud at a cost. Processor sharing techniques, in turn, affect the applications' processing delay on a local edge server depending on the number of application modules running on the same server. The fog orchestrator copes with local server congestion by offloading part of computation to the cloud trading off processing delay for a finite budget. Such problem can be described in a convex optimisation framework valid for a large class of processor sharing techniques. The optimal solution is in threshold form and depends solely on the order induced by the marginal delays of N fog applications. This reduces the original multidimensional problem to an unidimensional one which can be solved in O(N-2) by a parallelised search algorithm under complete system information. Finally, an online learning procedure based on a primal-dual stochastic approximation algorithm is designed in order to drive optimal reconfiguration decisions in the dark, by requiring only the unbiased estimation of the marginal delays. Extensive numerical results characterise the structure of the optimal solution, the system performance and the advantage attained with respect to baseline algorithmic solutions.