The Simulation And Research Of The Queuing Theory And Renewal Processes With Pare To Distribution

With the continuous development of the world, we have gradually entered the era of big data. On the one hand the number of data becomes bigger and bigger, on the other hand Internet traffic in the file size is also bigger and bigger. File transfering and processing has been widely used in the real life, so the study of flow file size is very important. We often come across a new file that is used to replace the old one, and this process is a renewal process, the Internet traffic in the file size always can be described by Pareto distribution. According to the problem of telecommunication traffic, we further analyze the cases of telecommunication traffic, some data cannot deal immediately, and then have congestion, this is actually a queuing problem, so we will find Pareto distribution in queuing theory also has practical significance. Since the real-life complexity and diversity of the renewal processes and queuing processes, these are difficult or nearly impossible to use mathematical formulas to represent,so using computer to simulate the renewal process and queuing system is a good solution.The main contribution of this paper is firstly using Matlab to simulate the renewal processes with Pareto distribution. Secondly, using Matlab to simulate the queuing theory with Pareto distribution. Thirdly, using the formula we can get the update number of alternating renewal process, the transition and probability of all the time points in the queuing system. Those simulation models set the same parameters for horizontal comparison. Firstly I create a simple simulation model, and then improve it, ultimately get more complex models, I want to do a comparison between each study time point and the point system change the pitch of the sate transition matrix, draw the image for analyzing and getting conclusion. So that we can know the system runs regularly,reasonable arrangement resources, improves efficiency, achieves the purpose of improving the overall system performance.