Broadband network access is typically managed by Broadband Network Gateways (BNGs), which can be implemented as a Virtual Network Function (VNF). This paradigm shift is caused by network softwarization and allows the BNG to be deployed on commodity hardware, significantly reducing capital expenditure (CAPEX). But packet processing operations and complex Quality of Service (QoS) policies make it difficult to provide low and predictable latency at scale for a large number of subscribers. To improve performance, parallel queues at the Network Interface Card (NIC) and multiple dedicated CPU cores for packet processing are used, processing 50 million packets per second on commodity x86 hardware. How to guarantee latency, however, remains unclear. In this study, we conducted testbed-based experiments on a VPP/DPDK implementation of the BNG to benchmark its performance. Our findings reveal how latency and its variation increase with background traffic, and we analyze a parameter that contributes to a trade-off between throughput and latency. We also examine the ability of the multi-core architecture to guarantee latency, at a cost of reduced port utilization. These observations influence the design goal of isolating subscriber traffic and highlight the suitability of software BNG for guaranteeing performance.