Abstract. Toeplitz matrices model a wide variety of problems in queueing theory. However, the algorithmic tools used in this field do not fully exploit the Toeplitz structure. In this paper, besides presenting a simple example that points out the role of Toeplitz matrices in queueing theory, we describe very recent results where some customary concepts, as displacement rank, Schur complement, FFT and fast polynomial computations, are exploited in order to devise very efficient algorithms for solving a wide class of queueing problems.

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