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The Erlangian approximation of Markovian fluid queues leads to the problem ofcomputing the matrix exponential of a subgenerator having a block-triangular,block-Toeplitz structure. To this end, we propose some algorithms which exploitthe Toeplitz structure and the properties of generators. Such algorithms allowto compute the exponential of very large matrices, which would otherwise beuntreatable with standard methods. We also prove interesting decay propertiesof the exponential of a generator having a block-triangular, block-Toeplitzstructure.

Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues