3GPP New Radio (NR) radio access technology operating in millimeter wave (mmWave) frequency band is considered as key enabler for Fifth-generation (5G) mobile system. Despite the enormous available bandwidth potential, mmWave signal transmissions suffer from fundamental technical challenges like severe path loss, sensitivity to blockage, directivity, and narrow beamwidth, due to its short wavelengths. To address the problem of quality degradation due to the line-of-sight (LoS) blockage by various objects in the channel, 3GPP is currently working on multi-connectivity (MC) mechanisms that allow a user to remain connected to several mmWave access points simultaneously as well as switch between them in case its active connection drops. In this paper, exploiting the methods of stochastic geometry and queuing theory we propose a model of 5G NR base station (BS) serving a mixture of unicast and multicast traffic. MC techniques is proposed to be used for cell-edge users. The proposed model is validated against computer simulations in terms of session drop probabilities and system resource utilization metrics. Our findings are illustrated with a numerical example. © 2020, Springer Nature Switzerland AG.