The rapid deployment of the fifth generation (5G) of wireless systems since 2020 is profoundly transforming the telecommunication area, paving the way for new-generation networks that include more devices and services, are more reliable and enable faster communication. The network slicing (NS) technology, considered as one of the 5G systems’ key features, allows the operation of several virtual networks called network slice instances (NSIs) on top of the same physical infrastructure, e.g. a base station. NSIs are specifically built to provide unique service types, i.e. the guaranteed bit rate (GBR), the best effort with minimum guaranteed (BG) or the best effort (BE). Furthermore, ensuring a satisfactory quality of service (QoS) level under NS technology is an important task, that may require to use the NSIs’ isolation concept. In this paper, a queueing system model for analyzing the operation of three 5G NSIs under a preemption-based scheduler maintaining the required QoS levels is proposed. The system’s key performance indicators (KPIs) are defined and computed. A numerical example of the system’s functioning is provided. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.