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Virtualization as one of the leading technologies has assisted datacenters to cloudify their products and provide versatile platforms and variety of Internet services. This technology also has facilitated agile deployment of complex Internet services such as Cloud-based multi-tier applications. However implementing multi-tier applications assists providers to set up flexible and scalable services, deploying such applications in virtualized environments faces challenges, which harden collocation of disparate multi-tier applications in a shared environment. In this article, we propose a placement strategy to consolidate multi-tier applications' tiers in a virtualized datacenter regarding workload demands of individual tiers, utilization of physical hosts' resources and operational status of virtual machines. The placement strategy identifies over-utilized hosts based on the birth--death stochastic process and ranks tiers based on Data Envelopment Analysis-Analytic Hierarchy Process modeling to be placed on target hosts. A prioritized tier will be placed on an appropriate host though least operational interference with hosted tiers incurred. The efficiency of the proposed model is evaluated using a series of in-depth experiments. We introduce results derived from quantitative and qualitative analyses that are useful for multi-tier applications placement in virtualized datacenters. Simulation results reveal that the proposed solution excels in terms of both load distribution and energy consumption in the datacenter, while the number of unnecessary migrations and consecutive Service Level Agreement violations is considerably reduced. [ABSTRACT FROM AUTHOR]