Communication networks support an increasing number of classes of service (CoS). Admission control strategies can be planned within the Markov decision process (MDP) framework; with the linear programming (LP) formulation of the MDP, class level requirements are explicitly controlled. Scalability problems with respect to the number C of CoSs arise with the standard LP formulation. This note proposes an alternative LP formulation, which is more scalable: the problem size reduction is O((C + 1)(2) /2(C)).