In this paper, we present an analytical model to characterize the average queuing delay for non-orthogonal multiple access (NOMA) downlink system by taking the outage event into account such that the user fails either decoding its own signal or performing SIC for the signals of other users at the receiver when the SINR is lower than a predefined outage threshold. The departure process of the queuing model is characterized by obtaining the first and second moment statistics of the service time that depends on the resource allocation strategy, the packet size and channel distributions. The proposed model is utilized to obtain the optimum power allocation that minimizes the maximum of the average queuing delay (MAQD) for a two-user network scenario. The Monte Carlo simulation experiments are performed to numerically validate the model by providing MAQD results for both NOMA and orthogonal multiple access (OMA) schemes. The results demonstrate that the NOMA achieves lower latency for low SINR outage thresholds while its performance is degraded faster than OMA as the SINR outage threshold increases such that OMA outperforms NOMA beyond a certain threshold. Another important result is that the latency performance of NOMA is significantly degraded when the 5G NR frame types having wider bandwidth are utilized. The results provide powerful insights for queuing delay analysis of 5G services.