Delay-constrained utility maximisation in multi-hop random access networks

Multi-hop random access networks have received much attention due to their distributed nature which facilitates deploying many new applications over the sensor and computer networks. Recently, utility maximization framework is applied in order to optimize performance of such networks, however proposed algorithms result in large transmission delays. In this paper, we will analyze delay in random access multi-hop networks and solve the delayconstrained utility maximization problem. We define the network utility as a combination of rate utility and energy cost functions and solve the following two problems: 'optimal medium access control with link delay constraint' and, 'optimal congestion and contention control with end-to-end delay constraint'. The optimal tradeoff between delay, rate, and energy is achieved for different values of delay constraint and the scaling factors between rate and energy. Eventually linear and super-linear distributed optimization solutions are proposed for each problem and their performance are compared in terms of convergence and complexity. Index Terms — Utility function, proportional fairness, convex optimization, feasible region, Dummy packet.