Petri Nets Formalization of Map/Reduce Paradigm to Optimise the Performance-Cost Tradeoff

Nowadays, the world around us is built up on more and more unstructured data every day. However, performing a longitudinal analysis of these data becomes a Big-Data problem that cannot be tackled with traditional tools, storage or processing infrastructures. One of the main contributions to address this matter has been the Hadoop framework (which implements the Map/Reduce paradigm), especially when used in conjunction with Cloud computing environments. This paper presents a formalization of the Map/Reduce paradigm which is used to evaluate performance parameters and make a trade-off analysis of the number of workers versus processing time and resource cost. We have used Prioritised -- Timed Coloured Petri Nets to obtain complete and unambiguous models of the system behaviour as well as CPNTools to evaluate the correctness of the system using state space exploration and for performance evaluation. The resulting formal model is evaluated with a real social media data Hadoop-based application and it is validated by carrying out experiments on a real private Cloud environment. Results show that the proposed model enables to determine in advance both the performance of a Map/Reduce-based application within Cloud environments and the best performance-cost agreement.