With the increase of network scale and complexity, network failure is inevitable. Interconnection networks require sustained and dependable operation, along with efficient routing algorithms for data transmission between processors. Fault-tolerant routing, particularly with the existence of independent spanning trees (ISTs), is essential. The 3-ary n-cube network \((Q^{3}_{n})\) , an extension of the hypercube, offers properties such as low vertex degree, edge symmetry, regularity, and ease of implementation. In this paper, we focus on constructing 2n ISTs in \(Q^{3}_{n}\) and develop a fault-tolerant routing system based on them. Simulated data show increasing transmission success rates with higher dimensionality, nearly reaching \(100\%\) . Although the analysis is done for a particular regular network \((Q^{3}_{n})\) , the outcome can serve as a useful reference, and can shed light on the effectiveness of the fault-tolerant communication for a large group of cube-based systems.