Transient Analysis of a Smart Stochastic Model for Tube-wells Integrated with Underground Pipelines for Sustainable Agriculture

The consistent supply of water for irrigation is essential in agriculture to enhance the production. Though several methods of irrigation are available but integration of tube-wells with underground pipelines has emerged as a promising solution to address the challenges of water scarcity, ensuring a reliable and available water supply for crop cultivation. By comprehensively assessing the factors influencing reliability and availability, this research aims to provide insights into optimizing the performance of these components, contributing to the sustainability of agricultural water delivery systems. This paper proposed a smart model for availability enhancement of tube-wells integrated with underground pipelines (TIUP). The study focuses on key components including tube-wells, pump sets, sensors, control units, Raspberry Pi units, centrifugal pumps, pipelines, and human resources. A mathematical model is proposed using birth-death process and Chapman-Kolmogorov differential-difference equations derived. All the failure and repair rates are considered as exponentially distributed while repairs are considered as perfect. The numerical solution of the proposed model is derived using Runge-Kutta 4th order. The effect of coverage factor on availability of system is analysed by changing the coverage factor, failure rates and repair rates. The findings are helpful for agricultural system designers and policy makers to make the provision for consistent water supply through providing reliable TIUPs.