General spin-up time distribution for energy-aware IaaS cloud service models

Cloud computing services provided over the Internet are realized by servers in physically distributed data centers that consume tremendous power for operational and maintenance purposes. To minimize energy consumption, modern cloud systems adopt intelligent sever power switching with thresholds based on the current system load and are bounded by the number of idle servers. The time taken to power on physical or virtual servers, known as the spin-up time, can significantly impact the delay incurred in service delivery and elasticity of real cloud platforms. In this paper, we model and assess the asymptotic performance of an energy-aware cloud data center assuming general distribution for server spin-up time. The waiting time of a newly arriving request is defined in the service-level agreement (SLA) and for each busy server, the fixation time distribution derived from an absorbing birth-and-death process characterizes the impact of thresholds. Simulation results show that the proposed model calculates the probability of SLA violation for different threshold values with less than 0.5% error.