Communications systems often have many types of users. Since the users share the same resource, there is a conflict in their needs. This conflict leads to the imposition of controls on admission or elsewhere. In this paper, there are two types of customers, GP (Guaranteed Performance) and BE (Best Effort). We consider an admission control of GP customer which has two roles. First, to guarantee the performance of the existing GP customers, and second, to regulate the congestion for the BE users. The optimal control problem for the actual physical system is difficult. A heavy traffic approximation is used, with optimal or nearly optimal controls. It is shown that the optimal values for the physical system converge to that for the limit system and that good controls for the limit system are also good for the physical system. This is done for both the discounted and average cost per unit time cost criteria. Additionally, asymptotically, the pathwise average (not mean) costs for the physical system are nearly minimal when good nearly optimal controls for the limit system are used. Numerical data show that the heavy traffic optimal control approach can lead to substantial reductions in waiting time for BE with only quite moderate rejections of GP, under heavy traffic. It also shows that the controls are often linear in the state variables. The approach has many advantages. It is robust, simplifies the analysis (both analytical and numerical), and allows a more convenient study of the parametric dependencies. Even if optimal control is not wanted, the approach is very convenient for a systematic exploration of the possible tradeoffs among the various cost components. This is done by numerically solving a series of problems with different weights on the costs. We can then get the best tradeoffs and the control policies which give them.