Congestion control for real time traffic is an important network measure to be handled in case of repeated event triggers, continuous packet re-transmissions, node interference, node deaths and node failures in Wireless Sensor Networks (WSNs). Network modelling for transmission of packets from source node to sink using probabilistic M/Pareto and Poisson processes have been examined in the past. The existing methodologies are deficit in designing a queuing framework considering other network parameters such as energy consumption and delay for alleviating congestion and thereby efficiently routing packets to sink by reducing packet drops. To overcome this fall back, a Minimum Weight Estimation for Mitigating Congestion during Real Time Burst Traffic (MWCBT) framework is proposed. This gives a precautionary solution against heavy traffic occupancy among the interim and sink-neighbouring nodes in WSNs is proposed. Routing of packets using a congestion-free path is required to increase the node lifespan. An optimal M/Pareto stochastic traffic generator is used in combination with traffic factors such as energy and delay to predict amount of traffic across nodes. A simpler congestion prediction mechanism is performed to control the occurrence of heavy-tailed traffic distributions. A torrent weight value for incoming traffic is generated at each node periodically that directs routing of data packets to sink. The devised MWCBT framework supervises real-time traffic congestion and is found to be more optimal than the existing approaches for network traffic modelling. The proposed approach achieves greater packet delivery ratio and less node congestion compared to the existing network modelling techniques.