Proportional Fair (PF) algorithm is known to achieve a good trade-off between efficiency and fairness by allocation opportunistically resources to users with good radio conditions, without sacrificing fairness considerations towards the other users of the system. On the other hand, Hierarchical Modulation (HM) is a means to increase the spectral efficiency of a given system by superposing an additional information stream over a basic one, by means of embedded constellations. This, in turn, results in a high resource utilization and hence overall system throughput. In this work, we quantify the system performance, obtained by jointly using PF with HM, for a realistic setting where users come to the system at random and leave it after a finite duration, upon the completion of their data transfers, and show that simple, cyclic Round Robin (RR) mechanism yields a better performance, along with simpler implementation