One of the ways to enable smooth coexistence of ultra reliable low latency communication (URRLC) and enhances mobile broadband (eMBB) services at the air interface of perspective 5G New Radio (NR) technology is to utilize preemptive priority service. In this paper, we provide approximate analysis of the queuing system with random resource requirements, two types of customers and preemptive priority service procedure. The distinctive feature of the systems – the random resource requirements – allows to capture the essentials of 5G NR radio interface but inherently increases the complexity of analysis. We present the main performance metrics of interest including session drop probability and system resource utilization as well as assess their accuracy by comparing with computer simulations. The developed model is not inherently limited to URLLC and eMBB coexistence and can be utilized in performance evaluation of 5G NR systems with priority-based service discipline at the air interface, e.g., in context of network slicing. Among other conclusions we explicitly show that both session drop and interruption probabilities of low priority traffic heavily depend not only on the intensity of high priority traffic but on stochastic characteristics of the resource request distribution. © 2020, Springer Nature Switzerland AG.