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Reliability and Energy-efficiency is one of the biggest trade-off challenges confronting cloud service providers. This paper provides a mathematical model of both reliability and energy consumption in cloud computing systems and analyses their interplay. This paper also proposes a formal method to calculate the finishing time of tasks running in a failure prone cloud computing environment using checkpointing and without checkpointing. To achieve the objective of maximizing the reliability and minimizing the energy-consumption of cloud computing systems, three resource provisioning and virtual machine (VM) allocation policies using the aforementioned mathematical models are proposed. These three policies are named Reliability Aware Best Fit Decreasing (RABFD), Energy Aware Best Fit Decreasing (EABFD), Reliability-Energy Aware Best Fit Decreasing (REABFD). A simulation based evaluation of the …