Prospective 5G New Radio (NR) systems offer unprecedented capacity boost by the ultradense deployments of small cells operating at mmWave frequencies, with massive available bandwidths. They will facilitate the provisioning of exceptionally demanding mission-critical and resource-hungry applications that are envisaged to utilize the 5G communications infrastructure. In this work, we provide an analytical framework for 5G NR system analysis in terms of queuing theory. We consider a multiservice queuing system with a limited resource with customers that demand varying amount of resource within their service time. Such an approach provides more accurate performance evaluation compared to conventional multiservice models. For the considered model, we propose a method that allows to calculate the stationary probability distribution to the specified accuracy. Our findings are illustrated with a numerical example. © Springer Nature Switzerland AG 2019.