Optimisation models and algorithms for multicast message routing and power control in wireless multihop networks

Abstract

The data capacity of a link within a wireless network depends in a nonlinear way on the communication resources allocated to it. Finding the optimal way to transmit data through a network consisting of many wireless devices can therefore be represented as a nonlinear optimization problem over network flow variables and communication resource variables. In this thesis we develop a nonconvex optimization problem for transmitting unicast and multicast messages through a time-slotted multi-hop wireless network. Multicast messages are handled in an optimal way through the use of network coding to allow data packets to be combined ensuring they are useful for multiple destinations. The benefits of network coding over other routing strategies are tested numerically. We look at simple networks to gain insight into the way various parameters affect the nonconvex behaviour before going on to develop algorithms which can be applied in a distributed manner, and make use of the coupled structure of the problem. We implement a subgradient method for solving the dual problem, and then look at ways to accelerate its convergence. We also investigate the behaviour and convergence of a simple but effective primal co-ordinate descent method before numerically investigating its performance.