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We consider admission and routing controls for a system of N parallel tandem queues with finite buffers as N becomes large, with the aim of minimizing costs due to loss. We obtain the fluid limit as N → ∞, and solve a related optimization problem. Asymptotically, for N large, the optimal cost and associated control take one of two forms, depending on the ratio between the cost of blocking an arrival at entry and discarding after service at the first queue.

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