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The 5th generation mobile networks (5G) based on virtualized and centralized radio access networks will require cost-effective and flexible solutions for satisfying high-throughput and latency requirements. The next generation fronthaul interface (NGFI) architecture is one of the main candidates to achieve it. In the NGFI architecture, baseband processing is split and performed in radio (RU), distributed (DU), and central (CU) units. The mentioned entities are virtualized and performed on general-purpose processors forming a processing pool (PP) facility. Given that the location of PPs may be spread over the network and the PPs have limited capacity, it leads to the optimization problem concerning the placement of DUs and CUs. In the NGFI network scenario, the radio data between the RU, DU, CU, and a data center (DC)—in which the traffic is aggregated—are transmitted in the form of packets over a convergent packet-switched network. Because the packet transmission is nondeterministic, special attention should be put on ensuring the appropriate quality of service (QoS) levels for the latency-sensitive traffic flows. In this paper, we address the latency-aware DU and CU placement (LDCP) problem in NGFI. LDCP concerns the placement of DU/CU entities in PP nodes for a given set of demands assuming the QoS requirements of traffic flows that are related to their latency. To this end, we make use of mixed integer linear programming (MILP) in order to formulate the LDCP optimization problem and to solve it. To assure that the latency requirements are satisfied, we apply a reliable latency model, which is included in the MILP model as a set of constraints. To assess the effectiveness of the MILP method and analyze the network performance, we run a broad set of experiments in different network scenarios.