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In this paper, a 1+1 server protection scheme is considered where two servers, a primary and a secondary processing server are used to serve ECG monitoring applications concurrently. The infrastructure is designed to be resilient against server failure under two scenarios related to the geographic location of primary and secondary servers and resilient against both server and network failures. A Mixed Integer Linear Programming (MILP) model is used to optimise the number and locations of both primary and secondary processing servers so that the energy consumption of the networking equipment and processing are minimised. The results show that considering a scenario for server protection without geographical constraints compared to the non-resilient scenario has resulted in both network and processing energy penalty as the traffic is doubled. The results also reveal that increasing the level of resilience to consider geographical constraints compared to case without geographical constraints resulted in higher network energy penalty when the demand is low as more nodes are utilised to place the processing servers under the geographic constraints. Also, increasing the level of resilience to consider network protection with link and node disjoint selection has resulted in a low network energy penalty at high demands due to the activation of a large part of the network in any case due to the demands. However, the results show that the network energy penalty is reduced with the increasing number of processing servers at each candidate node. Meanwhile, the same energy for processing is consumed regardless of the increasing level of resilience as the same number of processing servers are utilised. A heuristic is developed for each resilience scenario for real-time implementation where the results show that the performance of the heuristic is approaching the results of the MILP model.