Performance analysis and system optimization of an energy-saving mechanism in cloud computing with correlated traffic

<p style='text-indent:20px;'>Energy consumption is becoming a significant part of overall operational cost in cloud data centers. For the purpose of satisfying the Service Level Agreement (SLA) of cloud users while enhancing the energy efficiency in cloud computing systems, in this paper we propose an energy-saving mechanism with a sleep mode. Taking into consideration the traffic's correlation and the stochastical behavior of data arrival requests in a random cloud environment with the proposed energy-saving mechanism, we model the system as a MAP/M/<inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula>/<inline-formula><tex-math id="M2">\begin{document}$ N $\end{document}</tex-math></inline-formula>+<inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula> queue with a synchronous multi-vacation. Then, we present a theoretical basis for analyzing and evaluating the system performance by taking a state transition rate matrix in the steady state. Next, we investigate the change trends for the energy saving rate of the system and the average latency of tasks by carrying out numerical experiments. Moreover, we give a</p>