Abstract. Designers of large parallel computers and clusters are becoming increasingly concerned with the cost and power consumption of the interconnection network. A simple way to reduce them consists of reducing the number of network components and increasing their utilization. However, doing so without a suitable congestion management mechanism may lead to dramatic throughput degradation when the network enters saturation. Congestion management strategies for lossy networks (computer networks) are well known, but relatively little effort has been devoted to congestion management in lossless networks (parallel computers, clusters, and on-chip networks). Additionally, congestion is much more difficult to solve in this context due to the formation of congestion trees. In this paper we study the dynamic evolution of congestion trees. We show that, contrary to the common belief, trees do not only grow from the root toward the leaves. There exist cases where trees grow from the leaves to...