Present study reports the theoretical aspects of big data stream processing architecture and it's performance metric identification, performance optimization and related experiments. The proposed architecture is considered as a complex directed graph model with various real time computational elements as nodes and big data tuples as edges, forming a real time topology. The notions of hard time deadline bound computation on streaming big data tuple along with minimum performance guarantee of processing every tuple have been introduced in the present research. Time bound computation issues in the real time stream computing architecture have been improved by optimizing time deadline management through task forking models. An algorithm for optimization of throughput has been reported and the performance metrics of the proposed system has also been identified for proper analysis on the basis of queuing theories by expressing it through appropriate Kendalls notation. Experimental results, at the end, report considerable improvement of performance of the architecture by applying optimization algorithms on a standard dataset.