A number of analytical models for predicting message latency in k-ary n-cubes have recently been reported in the literature. Most of these models, however, have been discussed for adaptive routing algorithms based on deadlock avoidance. Several research studies have empirically demonstrated that routing algorithms based on deadlock recovery offer maximal adaptivity that can result in considerable improvement in network performance. Disha is an example of a true fully adaptive routing algorithm that uses minimal hardware to implement a simple and efficient progressive method to recover from potential deadlocks. This paper proposes a new analytical model of Disha in wormhole-routed k-ary n-cubes. Simulation experiments confirm that the proposed model exhibits a good degree of accuracy for various networks sizes and under different traffic conditions.