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Task scheduling on the heterogeneous distributed computing architectures have driven a new initiative on heuristics based paradigm to handle dynamic distributed workloads. Due to the expanding volume and the variety of Multi tasking work flows, task scheduling is often processed on scheduler. However existing scheduler has been modelled using map reduce architecture to task execution with map task and reduce task components. Despite of many advantageous, those model results in performance degradation such as make span and tardiness. In order to eliminate those issues, a new Heuristics based Dynamic Multi Task scheduling framework using Differential Equation for distributed computing has been proposed in this paper. The optimal scheduling solution has been generated using heuristics through differential equation that can quickly identify the efficient resource for execution. Heuristics of task scheduling include the ordering of system resources and predicting the worst case behaviour of the system on the map task and reduce task is based on the adaptive schemes. Further heuristics computes the priority of the task assigned to the resources on the task locality allocation strategies to particular resources. Finally trajectory of the task has been computed on aspect of best configuration on different communication modes towards its task propagation and efficient execution resource. Simulation results of the proposed architecture has been proven to be highly scalable on the proposed distributed computing architecture against traditional state of art approaches on the Google workloads and improves the make span and reduces the tardiness on the task execution.
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