Research On The Mean-field Theory And Macroscopic Computational Techniques In Large-scale Networks With Resource Management

The study of large-scale networks with resource management is always a considerable interesting topic in, such as, logistics and supply chain management, manufacturing systems, computer networks, internet of things, cloud computing, big data and so forth. Because the large-scale networks always possess stochasticity, bursty, concurrency, heterogeneity, complexity and so on, thus analysis of such a large-scale network is always more interesting, difficult and challenging. Based on this, this paper analyzes the large-scale networks with resource management within the single cluster and the resource management of work-stealing model within multiple clusters through the principle of bionics, builds a new real-time and dynamic control mechanism. For the two types of large-scale networks with resource management, this paper constructs a new type of real-time dynamic control strategy and mechanism, provides a macroscopic computational technique to analyze this large-scale complex stochastic networks, realizes the performance evaluation of large-scale networks and resource management system, which can be reasonable design and optimization control to large-scale networks.Firstly, for some basic issues of large-scale networks with resource management within the single cluster, we apply the bionics to establish a new stochastic model with an integrated mechanism of real-time and dynamic control through combining the supermarket models, with the work stealing models, and with the scheduling of common resources. We set up an infinite-dimensional system of differential vector equations and provide a calculation algorithm for computing the fixed point of the nonlinear equations. Furthermore, we demonstrate how the steady-state average queue length and the average sojourn time depend on the three real-time dynamic control strategy by the numerical examples, thus improve the performance of the system effectively.Secondly, for the resource management of work-stealing model within multiple clusters, we establish the work-stealing model within multiple clusters, and provide a new stochastic model with an integrated mechanism of real-time and dynamic control through combining the supermarket models and the work stealing models; We get the ordinary differential equations by using the mean-field theory, we analyze the system asymptotic independence by using the theory of martingale limit and give the fixed point algorithm of the system. And we provide the numerical experiments to analyze the system performance.Finally, we use the Qinhuangdao port coal berth and shipping management as an instance combined with the results of the fixed points in the large-scale networks with resource management within the single cluster. From the two aspects of arrival rate and the transfer rate, we analyze the port coal transportation network system resources through some numerical experiments.The results of this paper provide a macroscopic computational technique to research the large-scale networks with resource management and the network dynamic system, and the method of this paper can be applied to dealing with the broader field of large-scale practical network resource management issues.