One of the most crucial task during the design of a computing infrastructure is the decision about the proper amount of equipments required to handle a specific workload while satisfying a set of performance objectives. This problem is emphasized even more in actual computer infrastructure such as clouds, where the user can provision the resources very easily thanks to the use of virtual machines. If the system has to handle a low workload, resources can be consolidated together to reduce the costs. If however the workload is very high, resources must be replicated to gain an acceptable service level. In this paper we derive the impact on several performance indexes for both consolidation and replication when considering both open and closed workloads. In particular, we present an analytical model to determine the best consolidation or replication options that match given performance objectives specified through a set of constraints. Depending on the particular type of workload and constraints, we present either closed form expressions, heuristics or an iterative algorithm to compute the minimum number of resources required.
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