Research On The Resource Management Of The Supermarket Models Under Asynchronous Environment

Large network resource mangagenment has been the focus of the resaerch, as thewidely application of the cloud computing, cloud manufacturing and the large data.Supermaket models under asynchronous Markovian environments are the most effectivemathematical method to solve the large-network resource management.Firstly, we use the supermarket models under asynchronous environments to solvethe problem of large-scale network resource management. We set up an infinitedimensional system of differential vector equations, apply the operator semigroup toprovide a mean-field limit for the sequence of Markov processes who approaches a singletrajectory identified by the unique and global solution, discuss the system stability indetail by utilizing the method of coupling and develop an effective matrix-analyticalgorithm for computing the fixed point of the infinite-dimensional system of limitingdifferential vector equations.Secondly, the article set up the mean-field differential vector equations of therepairable supermarket models, and point out the method of calculating the fixed point oflimiting differential vector equations. At the same time, we analyze the influence to therepairable supermarket model under the mechanism with optional selection.Thirdly, we use the Qinhuangdao Coal Port as an instance combined with the resultsof the supermarket models under asynchronous environments and the the repairablesupermarket models. Some numerical examples are given for analyzing the performanceof the mean of stationary queue length in the port, and the expected sojourn time of anyarriving ship spending in the port. We put forward the main method to improve theefficency of resources management in the port is to improve the service rate of the berthand to chang the mechanism.Research on the supermarket models under asynchronous environment can providethe theoretical foundation in the fields of, such as computer application, supply chainmanagement, transportation and manufacturing services. Therefore, such supermarketmodels will have many important applications to our real life.