Admission control for combined guaranteed performance and best effort communications systems under heavy traffic

Communications systems often have many types of users. Since the users shar e the same resource, there is a conflict in their needs. This conflict lead s to the imposition of controls on admission or elsewhere. In this paper, t here are two types of customers, GP (Guaranteed Performance) and BE (Best E ffort). We consider an admission control of GP customer which has two roles . First, to guarantee the performance of the existing GP customers, and sec ond, to regulate the congestion for the BE users. The optimal control probl em for the actual physical system is difficult. A heavy traffic approximati on is used, with optimal or nearly optimal controls. It is shown that the o ptimal 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 tim e cost criteria. Additionally, asymptotically, the pathwise average (not me an) costs for the physical system are nearly minimal when good nearly optim al controls for the limit system are used. Numerical data show that the hea vy traffic optimal control approach can lead to substantial reductions in w aiting time for BE with only quite moderate rejections of GP, under heavy t raffic. It also shows that the controls are often linear in the state varia bles. The approach has many advantages. It is robust, simplifies the analys is (both analytical and numerical), and allows a more convenient study of t he parametric dependencies. Even if optimal control is not wanted, the appr oach is very convenient for a systematic exploration of the possible tradeo ffs 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 t he best tradeoffs and the control policies which give them.