Abstract

In this paper, we show that using the matrix-geometric solution method we can express the derivatives of the stationary queue length probabilities of the M/ PH/1/ K queue or the M/ PH/1/(∞, K) multiclass queue in terms of the stationary queue length probabilities of the M/ PH/1 queues with infinite buffer capacity. The results can be used in the optimization of networks consisting of nodes with finite buffers.

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