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A real-world topological network consists of multiple entrances along its source nodes. Routing appropriate percentages of pedestrians from these entrances to the particular available routes with relevant arrival rates will improve the network's performance. This paper presents a framework for finding the optimal arrival rates of pedestrians from all available entrances and routes to downstream nodes maximising the network's throughput. The calculation of the arrival rates and movement directions is based on M/G/C/C analytical and simulation models and the network flow model and considers the real distances of the entrances along the source nodes. The framework was tested on the Tuanku Syed Putra Hall, Universiti Sains Malaysia, Malaysia. Extensive analyses of the performances of its available nodes especially on the achievable optimal throughputs were documented and discussed. Quantitative results show that the hall's throughput is optimised when pedestrians' arrival rates to all the available entrances and their movement directions are controlled within certain ranges. [ABSTRACT FROM AUTHOR]