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In this paper we introduce an optimized real time scheduling algorithm for tasks allocation in grid environment. The modified RQSG algorithm is an optimized algorithm that is being improved using processing node and processing power parameters. The proposed algorithm allocates group jobs with prioritization rather than RQSG algorithm and also has dependent nodes in which the tasks are being done with less complexity as a set of output edges for each node. We have decreased the source loss time in proposed algorithm using a new technique and also have increased the efficiency by choosing various weighting positions of nodes in comparison with similar algorithms. With sources prioritized allocation, we have evaluated the requested times and the answers and thus optimized final processing time for task allocation. In comparison with standard RQSG algorithm, the weight and communication cost parameters have been increased in dependent tasks in modified RQSG algorithm and this has caused decreased makespan in qualification functions. By using prioritization queues and weight setting in priority functions, we have optimized the loss time in multi-face graphs with higher time complexity.