Node starvation wireless sensor network (WSN) is a critical factor that affects the overall performance in a typical multi-hop linear network especially in an extensive scale network. The unfairness of sharing network resources with all source nodes in a multi-hop linear network amplifies the node starvation that often results in passive nodes in a network. This factor becomes critical with the increasing network density, aggressive data transfer, single destination node and inadequate data scheduling. This paper highlights the Delayed acknowledgement timeout for flat one-tier throughput critical application model (DAT-FTCAM) a mathematical fairness model that ensure maximum throughput fairness for pipeline network scenario. The DAT-FTCAM enables the users to calculate the maximum delayed acknowledgement timeout for transmission control protocol (TCP) proportional to the travel time or difference between a source and a destination node. The implementation of DAT-FTCAM technique with modified TCP parameters on NS2 has revealed a network fairness index of above 0.99 with optimum network performance in a scalable pipeline network. The DAT-FTCAM decreases data packet collision and eliminates passive nodes in a pipeline network with optimum throughput fairness.