Network slicing is expected to become an integral part of future 5G systems providing a simple mechanism for physical network operators to diversify their business models. New Radio (NR) technology operating in millimeter wave (mmWave) band is one of the critical bearers for this functionality, providing extraordinary capacity at the air interface. This paper provides a mathematical tool for assessing the upper and lower bounds of NR BS density needed to maintain the requested slice rate guarantees. The upper bound corresponds to the full traffic isolation between slices while the lower one — to the full mixing of traffic from the slices. To this aim, we unite the tools of stochastic geometry and queuing theory formulating a performance evaluation framework that allows assessing the rate violation metrics in a dynamic network slicing environment. The developed framework captures specifics of mmWave NR technology, including antenna directivity at the UE and NR BS sides, propagation and blockage losses, as well as the service process with location-dependent resource requirements. Our results show that for considered schemes, the operational regime of the system changes abruptly with respect to the density of NR BSs. The difference between full isolation and full mixing schemes becomes bigger in environments with high session arrival intensities that naturally require dense deployments. Thus, at the initial market penetration phase, full isolation can be used without compromising the network performance. However, at mature stages, more complex schemes are needed to reduce the capital expenditures of the operators. © 2021 Elsevier B.V.