The application of random rounding with late groups of late clients was studied. The implementation of Robbins-Monro random approximation has been modified to be usable in the presence of late groups of late customers. Two loss regimes are presented for an accurate description of the proposed procedure. Each customer comes after specific time intervals with the stage of the next customer being exact according to the previous customer's score, where customer service time is assumed to be a discrete random variable. Some applications of the procedure are presented where the analysis of its results is obtained. The most important outcome is increased procedure efficiencies by increasing service time distributions as well as customer service times. This new mode can be applied to increase the number of clients served as the number of groups served will also be increased. The results obtained seem acceptable. In general, our proposal can be used in other stochastic approximation procedures to increase production in many fields such as medicine, computer science, industry, and applied science