This paper presents a new processor allocation approach called “a generalized k-Tree-based model” to perform dynamic sub-system allocation/ deallocation decision for partitionable multi-dimensional mesh-connected architectures. Time complexity of our generalized k-tree-based sub-system allocation algorithm is O(k⁴2^k(N_A +N_F )+k²2^2k) for the partitionable k-D meshes and O(N_A +N_F ) for the partitionable 2-D meshes, where N_A is the maximum number of allocated tasks, N_F is the corresponding number of free sub-meshes, N is the system size, and N_A +N_F ⩽ N. Most existing processor allocation strategies have been proposed for the partitionable 2-D meshes with various degrees of time complexity and system performance. In order to evaluate the system performance, the generalized k-Tree-based model was developed and by simulation studies the results of applying our k-Tree-based approach for the partitionable 2-D meshes were presented and compared to existing 2-D mesh-based strategies. Our results showed that the k-Tree-based approach (when it was applied for the partitionable 2-D meshes) yielded the comparable system performance to those recently 2-D mesh-based strategies.