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In this paper, the authors consider an m-node tandem queue (queues in series) with a Poisson arrival process and either deterministic or non-overlapping service times. With the assumption that each node has a finite buffer except for the first node, they show the non-increasing convex property of stationary waiting time with respect to the finite buffer capacities. They apply it to an optimization problem which determines the smallest buffer capacities subject to probabilistic constraints on stationary waiting times.
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