Complexity of Memory-eecient Kronecker Operations with Applications to the Solution of Markov Models

We present new algorithms for the solution of large structured Markov models whose innnitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shuue-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobi-style and Gauss-Seidel-style methods with appropriate multiplication algorithms. Our main contribution is to show how solution algorithms based on Kronecker expression can be modiied to consider probability vectors of size equal to the \actual" state space instead of the \potential" state space, thus providing space and time savings. The complexity of our algorithms is compared under diierent sparsity assumptions. A nontrivial example is studied to illustrate the complexity of the implemented algorithms.