Performance Analysis Of Idle Energy In Cloud System With One Compute Node Based On Discrete Time Queuing Theory

With the rapid development of cloud computing, the number and size of data centers are also growing rapidly, but at the same time, the problem of energy consumption is more prominent. The introduction of off/sleep technology can be a good solution to the problem of the idle energy which is generated by frequently opening and closing the compute node. An important problem in off/sleep technology is how to configure the value of the delay timer and other parameters to make the performance of the system optimal. The discrete-time queuing theory is introduced to mathematical modeling and performance analysis of idle energy in off/sleep technology of cloud system with a compute node and the dependency relationships between configuration parameters and performance measures of off/sleep technology in cloud computing is studied in this paper. The analysis results of this paper provide theoretical bases for the parameter configuration of off/sleep technology in cloud computing.Firstly, the mathematical modeling of off/sleep technology is built. We introduce the discrete-time queuing theory on the basis of summarizing the working principle of a compute nodes in off/sleep technology of cloud computing, a compute node and the tasks request of off/sleep technology are abstracted into a service desk and customer reach of discrete-time queuing theory, the starting time of the compute node is abstracted into period of setup, the closing time of the compute node is abstracted into period of closing, the delay closing time of the compute node is abstracted into period of close-delay, the abstract process of mathematical model in off/sleep technology of cloud system is completed.Secondly, aiming at the randomness of task request in cloud system, the performance analysis based on Geom/ G/ 1 discrete-time queuing model was completed. Based on the principle of off/sleep technology, the arrival interval of stochastic tasks in cloud system was portrayed as geometric distribution with after-effect, assuming that the processing time of stochastic tasks obeys normal distribution, we only study a single compute node with infinite buffer space of compute nodes cluster in cloud system, and the mechanism of setup、close delay、close down is introduced, the Geom/ G/ 1 discrete-time queuing model with setup mechanism and delayed vacation is built. Using the embedded Markov chain method to derive the mathematical expressions of system performance measures, such as average response time, average number of waiting tasks, energy saving rate, switching rate of system state and system efficiency. The numerical examples are intuitively given to analyze the dependence of system idle energy performance measures and configuration parameters.Finally, aiming at the burst of task request in cloud system, the performance analysis based on Geom/ G/ 1ξ discrete-time queuing model was completed. Considering the burst of stochastic task request on the basis of the Geom/ G/ 1 discrete-time queuing model with setup mechanism and delayed vacation, we introduce batch arrival mechanism, a Geom/ G/ 1ξ discrete-time queuing model with setup mechanism 、delayed vacation、close down is built and the batch size ξ obeys Pareto( c, δ) distribution. Using the embedded Markov chain method to complete the analysis of the queuing model, the mathematical expressions of system performance measures are derived, such as average number of waiting tasks, energy saving rate, switching rate of system state and system efficiency. We intuitively discuss the dependence of system idle energy performance measures and configuration parameters through the numerical examples and analyze the impact of burst size on system idle energy performance measures.