Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues
For researchers in queueing theory and applied probability, this provides efficient computation for large-scale fluid queue models where standard methods fail.
The paper addresses the problem of computing the matrix exponential of large block-triangular block-Toeplitz matrices arising from Erlangian approximation of Markovian fluid queues. It proposes algorithms that exploit the Toeplitz structure to handle matrices that are untreatable with standard methods, and proves decay properties of the exponential.
The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a generator having a block-triangular, block-Toeplitz structure.