  In this tutorial paper, a comprehensive survey is given on several major
systematic approaches in dealing with delay-aware control problems, namely the
equivalent rate constraint approach, the Lyapunov stability drift approach and
the approximate Markov Decision Process (MDP) approach using stochastic
learning. These approaches essentially embrace most of the existing literature
regarding delay-aware resource control in wireless systems. They have their
relative pros and cons in terms of performance, complexity and implementation
issues. For each of the approaches, the problem setup, the general solution and
the design methodology are discussed. Applications of these approaches to
delay-aware resource allocation are illustrated with examples in single-hop
wireless networks. Furthermore, recent results regarding delay-aware multi-hop
routing designs in general multi-hop networks are elaborated. Finally, the
delay performance of the various approaches are compared through simulations
using an example of the uplink OFDMA systems.
