Abstract: The explosive growth of demands on huge process imposes a crucial burden on computation, storage, and communication in data centers, that so incurs wide operational expenditure to data center suppliers. Therefore, Price decrease has become Associate in Nursing rising issue for the longer term huge data era. All totally different from customary cloud services, one in each of the foremost choices of huge data services is that the tight coupling between data and computation as computation tasks is also conducted provided that the corresponding data is obtainable. As a result, 3 factors, i.e., task assignment, data placement and data movement, deeply the operational expenditure of data centers. Throughout this paper, we tend to tend to unit of measurement meant to see the worth decrease downside via a joint improvement of these three factors for big data services in geo-distributed data centers. To elucidate the task completion time with the thought of every data transmission and computation, we tend to tend to propose a two-dimensional stochastic process and derive the standard task completion time in closed-form. Moreover, we tend to tend to model the matter as a mixed-integer non-linear programming (MINLP) and propose economical resolution to correct it. The high efficiency of our proposal is valid by thorough simulation primarily based studies Keywords— Nonlinear Programming, Big Data, Computer Centres, Integer Programming, Minimisation, Mixed Integer Nonlinear Programming, Cost Minimization, Data Centers, Big Data Services, Operational Expenditure, Task Assignment, Big Data