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As parallel computing systems increase in size, the interconnection network is becoming a critical subsystem. The current trend in network design is to use as few components as possible to interconnect the end nodes, thereby reducing cost and power consumption. However, this increases the probability of congestion appearing in the network. As congestion may severely degrade network performance, the use of a congestion management mechanism is becoming mandatory in modern interconnects. One of the most cost-effective proposals to deal with the problems derived from congestion situations is the Regional Explicit Congestion Notification (RECN) strategy, based on using special queues to totally isolate the packet flows which contribute to congestion, thereby preventing the Head-of-Line (HoL) blocking effect that these flows may cause to others. Unfortunately, RECN requires the use of source-based routing, thus not being suitable for interconnects with distributed routing, like InfiniBand. Although some RECN-like mechanisms have been proposed for distributed-routing networks, they are not scalable due to the huge amount of control memory that they require in medium-size or large networks. In this paper, we propose Distributed-Routing-Based Congestion Management (DRBCM), a new scalable technique which, following the RECN principles, totally prevents congestion from producing HoL-blocking in multistage interconnection networks (MINs) using tag-based distributed routing. Simulation results indicate that, regardless of network size, DRBCM presents small resource requirements to keep network performance at maximum level even in scenarios of heavy congestion, where it utterly outperforms (with a gain up to 70 percent) current solutions for distributed-routing networks, like the InfiniBand congestion-control mechanism based on injection throttling. Thus, DRBCM is an efficient, cost-effective, and scalable solution for congestion management.