Nonorthogonal multiple access (NOMA) is one of the key technologies for 5G, where the system capacity can be increased by allowing simultaneous transmission of multiple users at the same radio resource. The most of the proportional fairness (PF)-based resource allocation studies for NOMA systems assumes full buffer traffic model, while the traffic in real-life scenarios is generally nonfull buffer. In this paper, we propose User Demand-Based Proportional Fairness (UDB-PF) and Proportional User Satisfaction Fairness (PUSF) algorithms for user scheduling and power allocation in NOMA downlink systems when traffic demands of the users are limited and time-varying. UDB-PF extends the PF-based scheduling by allocating optimum power levels towards satisfying the traffic demand constraints of user pair in each resource block. The objective of PUSF is to maximize the network-wide user satisfaction by allocating sufficient frequency and power resources according to traffic demands of the users. In both cases, user groups are selected first to simultaneously transmit their signals at the same frequency resource, while the optimal transmission power level is assigned to each user to optimize the underlying objective function. In addition, the genetic algorithm (GA) approach is employed for user group selection to reduce the computational complexity. When the user traffic rate requirements change rapidly over time, UDB-PF yields better sum rate (throughput) while PUSF provides better network-wide user satisfaction results compared with the PF-based user scheduling. We also observed that the GA-based user group selection significantly reduced the computational load while achieving the comparable results of the exhaustive search.