In this thesis, we address the problem of minimizing the average delay of data pack-ets served by a transmitter on a static, point-to-point link. The transmitter dynamically chooses state-dependent admission and transmission rates, while adhering to average throughput and transmission power constraints. The transmitter is modelled as an infinite buffer Markov queue with adjustable arrival and service rates. Data packets arrive at the system according to a Poisson process with rate, Λ, and are admitted at a rate, λnwith 0≤ λn ≤ Λ, depending on the number, n, of data packets present in the system. The packet size is assumed to be exponentially distributed, and the controller chooses a transmission rate, µn, at most equal to a maximum value, M, depending on the current backlog, n, in the system. The objective is to minimize the average delay of data packets in the system subject to a throughput lower bound constraint, while satisfying an upper bound on the average transmission power. This constrained MDP problem is solved using a Lagrange relaxation approach and analysed for the cases with throughput and power constraints that are achievable with equality by appropri-ate values of the Lagrange multipliers. A procedure is developed, based on explicit formulae, using which optimal admission and service rates as a function of the packet queue length are obtained.