Delay control for CDF scheduling using Markov decision process

We consider the problem of controlling the user service delays for a system that employs a scheduling scheme based on Cumulative Density Functions (CDF) of user channels in a correlated Rayleigh fading environment. We first formulate and solve this control problem as a Markov Decision Process (MDP) on the system state space formed by the user channel conditions and delay times. The MDP formulation, however, has prohibitively high complexity for systems with typical number of users. We then propose an approximation to the MDP formulation that can achieve performance close to MDP optimal solution but has much lower complexity for large systems.