A new LP formulation of the admission control problem modelled as an MDP under average reward criterion

The admission control problem can be modelled as a Markov decision process (MDP) under the average cost criterion and formulated as a linear programming (LP) problem. The LP formulation is attractive in the present and future communication networks, which support an increasing number of classes of service, since it can be used to explicitly control class-level requirements, such as class blocking probabilities. On the other hand, the LP formulation suffers from scalability problems as the number C of classes increases. This article proposes a new LP formulation, which, even if it does not introduce any approximation, is much more scalable: the problem size reduction with respect to the standard LP formulation is O((C+1)(2)2(C)). Theoretical and numerical simulation results prove the effectiveness of the proposed approach.