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We propose a close-loop queueing model of a multiprotocol label switching (MPLS) switch with the different label-setup and release policies, supporting both traffic-driven and topology-driven connection setup procedures. This model can emulate the behavior of TCP under the MPLS switch when the maximum window size is sustained and the packet loss rate is negligible. From the proposed flow-based MPLS switch model, one can clearly observe the competition of multiple IP flow for limited labels, and how the label-setup policy and the label release policy affect the system performance. We find that Norton's theorem can be applied to solve this sophisticated queueing model. Therefore, with very limited computational complexity with respect to the number of IP flows or labels, the proposed mathematical model and the approximation of label competition can be used to obtain the desired performance metrics, such as the throughput, the label-setup rate, and the channel utilization. Finally, the trade-off among performance metrics can be observed as well.