Evolution of Distributed File System and Hadoop: A Mathematical Appraisal

The fast growing technology has left a great impact on the human life. Many traditional systems are either replaced or running in parallel with their electronic counterpart. As for example: - the traditional postal system is now nearly replaced by mobile phones and emails. The electronic system is providing more functionalities than their traditional counterparts. Due to social media, peoples may communicate with each other, share their thoughts and moments of life in form of texts, images or videos. On the other hand, to enhance technologies and knowledge many research activities are propelled and data from different sources are gathered in large volume for further analysis. In short today’s world is surrounded with large volume of data in different form. This put a requirement for effective management of these billions of terabytes of electronic data generally called BIG DATA. The effective management must be based on proven mathematical concepts so that chance of casualties may be reduced. The study objective of this is to provide a mathematical appraisal for evolution of distribution of file data and explains some basic solution of primitive problems based on probability theory. The probability theory helps us to formalize the basic tree like architecture of distributed file system if we try to solve the problem like Big Data.