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These two massive systems work at scales, in terms of storage and computing power, which are not comparable to our everyday devices. As such, they require state-of-the-art technology to constantly evolve and meet our increasing demand. The interconnection network is the backbone of these systems, since it must provide efficient communication among the nodes that compose the whole system, otherwise becoming the entire system bottleneck. As multiple applications and services may use subsets of the system at the same time, interconnection networks must prevent excessive degradation for latency-sensitive applications. To this end, differentiated services are used to provide fair network access that considers bandwidth and latency requirements for each application. In this paper, we extend the switch architecture of next-generation BXI networks (hereafter called BXIv3) to incorporate arbitration tables so these networks can provide quality of service (QoS) to applications and services running on both SCs and DCs. Our proposal has been implemented in a network simulator, which models the behavior of a BXIv3 network. We have used several traffic patterns and arbitration table configurations to conduct a set of simulation experiments for the evaluation of our solution. The obtained results show that our proposal achieves accurate bandwidth allocation with differentiated latencies. 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