Analysis of the loss probability of the map/g/1/k queue part ii: approximations and numerical results

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Abstract
In this paper we propose an approximate method for the evaluation of the loss probability of a MAP/G/1/K queue. The method consists essentially of a truncated partial fraction expansion based on a spectral decomposition of a matrix generating function. The accuracy of the resulting approximation depends on the number of poles of the generating function that are considered Through many numerical examples, our method is shown to yield quite accurate results: in fact the proposed approximations are asymptotically exact as the buffer size increases, but they turn out to be accurate even for small buffer sizes (e.g. a few units or tens of buffer positions). Moreover, the computational effort implied by the proposed approximations and the simplifications brought about by special MAPs are discussed The asymptotic correctness of the proposed approximations of the loss probability as the buffer size increases is proved in a companion paper [1]