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In prior work, we proposed a hybrid architecture that complements the connectionless Internet with a high-speed, dynamically shared circuit-switched network for file-transfer applications. "Smallrdquo files are directed to the connectionless network while for "largerdquo files, a high-speed circuit setup is attempted. If the attempt is unsuccessful (because all circuits are already in use), the application will fall back to using the connectionless path. This paper addresses the question of how to select appropriate values for operational parameters in this hybrid architecture. Specifically, we study the questions of what sized files to direct to the circuit-switched network and how much bandwidth to allocate per file transfer. To answer these questions, we construct a model of this hybrid architecture by combining the Erlang-B call blocking model with TCP delay models. Our model captures a combination of utilization and delay considerations in the selection of minimum file size above which transfers should be directed to the circuit-switched network. The optimal per-call circuit rate and the optimal minimum file size are determined to maximize the benefits of using the circuit network, which is quantified with an average-delay-reduction metric.