The intensification of mobile broadband services and user experience is explicitly dependent on increased battery life of user equipment (UE) and minimized delay in service. In 5G New Radio (NR), in addition to Discontinuous Reception (DRX) scheme, Bandwidth Part (BWP) switching plays a significant role in reducing UE power consumption. The dynamic bandwidth operation in BWP switching is power efficient as UE can adapt its operating bandwidth based on the traffic arrival. In this work, BWP switching based DRX mechanism is modeled as an MX/G/ 1 queue to trade-off between quality of service (QoS) and power saving in UE in 5G NR. Analytical and numerical results on the proposed model show it to be promising in minimizing power consumption and reducing delay in service of UE.